MCAT Physics Flashcards
A man walks 30m east and then 40m north. What is the difference between his traveled distance and his displacement?
A) 0 m
B) 20 m
C) 50 m
D) 70 m
B
Using the pythagorean theorem (a^2 + b^2 = c^2), calculate the magnitude of the man’s displacement. His total distance is equal to 30+40=70 m. Therefore, the difference between the two is 20 m. (900+1600=2500; square root of 2500 is 50. 70-50=20 m).
While working at a beer factory, you cleverly devise a 6 pulley system to aid in your hauling of boxes. The system has an efficiency of 80%. Imagine you are lifting a mass of 200kg. What is the effort required to lift the load 4m?
A) 200N B) 400N C) 600N D) 800N E) None of the above
B
The equation here is: efficiency = Wout / Win OR (load)(load distance) / (effort)(effort distance). Since the load is moving 4 meters (which is the load distance), the effort distance is 6 times this. For the load to move 4 meters, all 6 ropes of the pulley must move 6 meters, totaling 24 meters. Last, the load is the force of the box being lifted, which is its mass in kg times acceleration due to gravity. Plugging this all into the equation, along with the given 80% efficiency, yields: 0.8 = (200kg x 9.8 m/s^2)(4m) / (effort)(24m) Effort then = 408N so 400 is the closest answer.
What force will the boy need to pull on the rope to lift the weight?
Boy is pulling down on a double pulley, no crazy designs. One rope wrapped around 2 pulleys. Creating 4 ropes bearing tension. 10kg weight with (g = 10 m/s^2)
A) 10 N
B) 20 N
C) 25 N
D) 100 N
C
This is a “Double Block Tackle” and as there are four ropes lifting the 10 kg (100 N weight), each has a tension of 100/4 = 25 N. The only catch is he needs to pull four times the rope length than would be required to simply lift the weight.
A 30kg cart traveling due north at 5 m/s collides with a 50kg cart that had been traveling due south. Both carts immediately come to rest after the collision. What must have been the speed of the southbound cart?
A) 3 m/s
B) 5 m/s
C) 6 m/s
D) 10 m/s
A
Momentum is conserved. Since both carts come to rest, the total momentum must be zero. If the two carts are labeled A and B then:
MaVa = MbVb Vb = (30kg)(5 m/s) / (50kg) = 3 m/s
If the sum of all the forces acting on a moving object is zero, the object will:
A) Decelerate and stop
B) Accelerate uniformly
C) Change the direction of its motion
D) Continue moving with constant velocity
D
For something to change direction or accelerate there must be a net force acting on it (Newton’s 2nd Law). Also, Newton’s 1st Law states that an object in motion will stay in motion at constant velocity (a form of inertia) unless acted upon by a net (an unbalanced) force.
An MCAT book weighing 40 N is held in contact with the ceiling of the room by an upward force of 50 N. What is the magnitude of the normal force exerted by the ceiling on the book?
A) 0 N
B) 10 N
C) 50 N
D) 90 N
B
What are the forces on the book? The weight, 40 N, and the normal force, N are downward forces, and the only upward force is our 50 N push. Since the book is not accelerating vertically, the net vertical force must be zero. Therefore, 40 + n must be 50, which means n = 10 N.
The aorta of a 70 kg man has a cross section area of 3 square centimeters and carries blood with a velocity of 30 centimeters per second. What is the average volume flow rate?
A) 10 cm^3/s
B) 33 cm^3/s
C) 66 cm^3/s
D) 90 cm^3/s
D
Q = Av = (3.0 cm^2)(30 cm/s) = 90 cm^3/s.
The force of gravity between two bodies is:
A) Inversely proportional to the distance between them
B) Directly proportional to the distance between them
C) Inversely proportional to the square of the distance between them
D) Directly proportional to the square of the distance between them
C
The Law of Universal Gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The speed of a sound wave is 340 m/s and its wavelength is 10 cm. What is its frequency?
A) 3.4 Hz
B) 34 Hz
C) 340 Hz
D) 3,400 Hz
D
Using the equation v = h(or lambda) * f, we find that f = v / h(or lambda) = (340 m/s) / (0.1 m) = 3,400 Hz.
Consider the Law of Gravitation where the force of gravity F is:
F = G(m1m2/r2)
Which of the following represents the gravitational constant G in the fundamental dimensions of mass (M), length (L) and time (T)?
A) M-1L3T-2
B) M2L3T-2
C) M-1L-3T-2
D) M2L3T2
A
This is a classic example of dimensional analysis (DA). Expect to use DA to one degree or the other during the real MCAT. First, you should know that the unit of force is a newton which is also a kg m/s2 (even if you did not memorize that, it is easy to work out since F = ma so the units of F must be kg multiplied by acceleration which is m/s2). Of course the 2 m’s in the Law of Gravitation represent masses (M) and the r represents a distance or length (L). So we get:
F = G(m1m2/r2)
Now transferring to the fundamental quantities except for G:
MLT-2 = G(M)2L-2
Divide both sides by (M)2L-2 and isolate for G:
G = M-1L3T-2
… which is the same as m3kg-1s-2.
Water moves through a turbine in a dam, causing it to turn. The force of the water is 300 N, and the radius of the wheel is 20 m. What is the torque around the center of the wheel?
A) 60 N-m
B) 600 N-m
C) 6,000 N-m
D) 60,000 N-m
C
Assuming that the water stream is tangent to the wheel, it will be perpendicular to the radius vector at the point of contact. Therefore, the torque of the force of the water stream is Torque = r*F = (20m)(300 N) = 6000 N-m.
When a massive GameCube with an edge length of 0.5 m is 10 m below the surface of a body of water, the buoyant force it feels has magnitude F. When the top of the GameCube rises to a depth of 5 m, what is the magnitude of the buoyant force?
A) F/2
B) F
C) 2F
D) 4F
B
Since the GameCube is totally submerged at both depths, the buoyant force, B = pVg, is the same at both depths.
When two converging lenses of equal focal lengths are used together, the effective focal length of the combination is less than the focal length of either individual lens. The power of the lens combination will be:
A) Greater than the power of either individual lens
B) Less than the power of either individual lens
C) The same as the power of either individual lens
D) None of the above
A
Lens power is the reciprocal of the focal length: P = 1/f. If the effective focal length of the lens combination is less than the focal length of either individual lens, then the power of the combination must be greater than the power of either individual lens.
A baby can easily surpass 100 decibels. Which of the following part of a sound wave is increased to create such a loud cry?
A) The wave’s wavelength
B) The wave’s frequency
C) The wave’s amplitude
D) The wave’s period
C
Loudness is a measure of intensity or power per area. The area of the ear is fixed, but the power of the wave can be increased. Power is energy over time, or force times velocity.
Sound is a pressure wave. The force can be written in terms of pressure times area, and the velocity can be written in terms of speed over a bulk modulus. Together these give a power independent on frequency. The period, frequency, wavelength, and wavenumber all relate to one another through the phase velocity. If you are dependent on one of them, you are dependent on the rest.
A length of piping connects the rain gutters on a house roof to the drain in the ground. The house is 3 stories, or about 8 meters in height. If a hole forms in the pipe at the midpoint, approximately what will the velocity of the water be as it escapes through the hole? Ignore water flow and use kinematics.
A) 5 m/s
B) 9 m/s
C) 13 m/s
D) 19.6 m/s
B
The water will exit at a velocity which is proportional to the height it has fallen, according to the equation v = sqrt(2gh). This can be derived from the basic equation for velocity and displacement, v2 = 2a * s, where a is acceleration, and s is displacement (or in this case height). Thus, the height the water has fallen in this problem is 4 meters, and v = 8.85m/s, which we round up to 9.
A box is stationary on an inclined plane. As the angle of the inclined plane – determined by measuring from the horizontal – increases, the normal force:
A) Decreases nonlinearly
B) Increases nonlinearly
C) Does not change
D) Increases linearly
A
The only forces that act perpendicular to the incline are the normal force and the perpendicular component of weight. There is no acceleration perpendicular to the incline for this stationary object. The normal force is equal to the perpendicular component of the weight, which is given by mg cos. As the angle increases, the cosine of the angle must decrease. The graph of the normal force N vs o would show a curve, not a line and so the change is nonlinear.
An object undergoing simple harmonic motion is observed to have a time interval of 4 seconds between the two extremes of its displacement from equilibrium. What is the frequency of this motion?
A) 0.125 cycles/second
B) 0.25 cycles/second
C) 1.25 cycles/second
D) 4 cycles/second
A
Since it takes 4 seconds for the object to travel from one end of its displacement to the other (half a cycle), the time for a full cycle is 2(4 sec) = 8 sec. Thus frequency = 1/T = 1/8 = 0.125 Hz.
A 50N crate is set in motion. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.20. What is the difference between the force needed to initiate motion and the force needed to maintain motion?
A) 10 N
B) 15 N
C) 25 N
D) 125 N
B
Finitiating = (us)N ; And Fmaintaining = (uk)N
Fi - Fm= (us– uk)N = (0.50 – 0.20)(50 N) = 15 N
A car drives around a circular track at a constant speed of 20 m/s. If the track is flat and has a radius of 200 m, what is the acceleration of the car?
A) 2.0 m/s2
B) 4.0 m/s2
C) 6.0 m/s2
D) The car is not accelerating
A
The speed is constant but the direction of the car is constantly changing, thus the velocity is constantly changing, which in turn means the car undergoes acceleration. Since only the direction is changing, only the radial acceleration component is nonzero. The tangential acceleration component is zero.
ar = v^2/ r = (20 m/s)^2 / 200 m = 2.0 m/s2
The Sun emits extremely large amounts of energy through solar flares. Which of the following reactions results from alpha decay?
A) 214Pb -> 214Bi
B) 222Rn -> 218At
C) 210At -> 208Po
D) 263Sg -> 259Rf
D
Alpha decay results in the ejection of an alpha particle from the nucleus. The alpha particle contains two protons and two neutrons. The two protons would decrease the atomic number by two and the total mass number of the atom would decrease by four. The only choice that satisfies both of these requirements is D, 263Sg -> 259Rf.
A man rides his bike in a circular path at the park at a constant speed. Which of the following applies?
A) The velocity is constant since the speed is constant
B) The acceleration is zero since the speed is constant
C) The acceleration is not zero and is always directed tangent to the path
D) The acceleration is not zero and is always directed toward the center of the path
D
Choice A is false because the object’s direction of motion is always changing, and choice B is false because the velocity is not constant. The acceleration, termed centripetal, points toward the center of the circular path.
A group of hydrogen atoms emit specific wavelengths of light. The light spectrum is a result of:
A) Excited electrons dropping to lower energy levels
B) Particles being emitted as the hydrogen nuclei decay
C) The light wavelengths which are not absorbed by valence electrons when white light is passed through the sample
D) Energy released as H atoms form H2 molecules
A
The line spectra of atoms are the result of the photons emitted when excited electrons drop to lower energy levels.
A racecar travels in a circular path around the Daytona 500 track. The radius of the circular track is doubled and the speed of the car does not change. The required force to maintain the car’s motion is:
A) Quadrupled
B) Unchanged
C) Doubled
D) Halved
D
The centripetal force of the car is mv^2/r, where m is the car’s mass, v is the velocity, and r is the radius of the circular track. If we double the radius while keeping everything else uniform, the centripetal force will be halved because they are inversely proportional.
Three identical 12 ohm resistors are connected in parallel to a 8V battery. What is the total power dissipated in the circuit?
A) 18 W
B) 36 W
C) 16 W
D) 40 W
C
When resistors are in parallel, we can find equivalent resistance simply by using the equation:
(1/Req) = (1/R1) + (1/R2) + … + (1/Rn)
In this case, the equivalent resistance is: (1/Req) = (1/12) + (1/12) + (1/12) = 3/12
We find that Req = 4. We then input this into our equation for the power of a circuit
P = IV = V^2/R = 8^2/4 = 16W
The period of a simple pendulum can be increased by:
A) Increasing the length of the pendulum
B) Decreasing the length of the pendulum
C) Increasing the mass of the box
D) Decreasing the mass of the box
A
The period, T, is equal to:
T = 2(pi) sqrt(L/g)
Thus, the period is directly proportional to the square root of the length. Any increase in L will produce an increase in T. The mass of the box does not influence the period.
The constant k, which appears in the equation for Coulomb’s law, is equivalent dimensionally to which of the following?
A) N/C^2
B) N⋅m/C
C) N⋅C^2/m^2
D) N⋅m^2/C^2
D
The SI unit for force F is newtons N and for q, the SI unit is coulombs C and, of course, meters m is the SI unit for length/distance symbolized as r in Coulomb’s law.
Using Coulomb’s equation: F = kq1q2/r^2
We get in SI units: N = k (C)(C)/m^2 = k (C)^2/m^2
And so isolating for k: k = N•m^2/C^2
Expect questions requiring dimensional analysis on the real exam.
A 1kg ninja star is hung from the end of a vertical spring with a spring constant of 20 N/m. When the ninja star comes to rest, how far will the spring have stretched?
A) 0.05
B) 0.5
C) 2.0
D) 2.5
B
Once the ninja star comes to rest at the end of the spring, the upward force by the spring must balance the downward force of gravity. That is, kx = mg. Solving for x yields x = mg/k (1)(10)/(20) = 0.5 m.
The human body has an average temperature of 37°C. A person, with a fever of 40°C, would like to know what will be the temperature of her skin in an ice bath, after reaching a steady state. Which of the following equations can be used to create an analogous formula for heat transfer due to conduction?
A) d = r * t
B) V = I * R
C) F = ma
D) E = mc^2
B
At a first glance, one might think that none of these equations deal with heat. It is important to recall that heat is energy. Immediately one can rule out answer choices A and C, as they do not deal with energy. Taking a deeper look into equation D we can see Einstein’s famous equation states that the energy is equal to some constant squared. We can try to relate that with heat, by asking if heat is proportion to a single constant. We know that this is not true by 1.) ice melts at different rates depending on the temperature and 2.) chocolate and ice melt at different rates at the same temperature. We have parameterized heat based on ambient temperature as well as by the individual material. The remaining solution is choice B.
Lets confirm this be taking a further look into choice B. Ohm’s law says that the potential is directly related to the current by a resistance. This can be rearranged to have the current indirectly related to the potential through resistance, or directly related to the potential through the conductance, g.
The current is a charge rate, Q/t. If we replace charge with heat, we can obtain the thermal conduction formula. With the charge rate becoming a heat rate, the conductance becoming a heat conductance, and the potential difference becoming the temperature drop.
A tilt table test is used to verify if a patient has low pressure drops associated with syncope. The heart, of a horizontal patient, pumps blood at a mean arterial pressure of 90 mmHg (12 kPa). The patient faints as soon as the tilt table goes vertical, this means the blood acceleration equal the gravitational acceleration. If the heart rate does not increase to compensate for the change in angle, at what angle would the blood be pumping one half its horizontal pressure.
A) 0 degrees
B) 30 degrees
C) 45 degrees
D) 60 degrees
B
Pressure is force over area. The cross-sectional area of the circulatory system is not changing. The direction of the force appears to be changing. But the blood is still flowing orthogonal to the area, creating the same pressure due to the heart. The only additional element is that gravitational force is being applied.
This additional gravitation force opposes the heart force by a factor of sin(theta) times its weight. We are told that the blood acceleration is equal to g. All we need to find now is when the sin is equal to one half. This will yield a pressure of one half of the horizontal value. This occurs at 30 degrees.
Radiation therapy uses high energy photons to ionize the DNA in malignant cells. If UVB light has enough energy to create pyrimidine dimers, what part of the electromagnetic spectrum can be used for its curative, higher energy effects.
I. X-rays and gamma rays
II. Radio waves and micro waves
III. NIR and Green light
A) I only
B) II only
C) I and II
D) II and III
A
We are looking for something with more energy than UVB radiation. We 1st need to know where UVB radiation lies on the electromagnetic spectrum. Recall that UVB is ultra violet, meaning that it exists just beyond the visible color violet.
What helps me remember the EM spectrum is the last word of each part. We have UV rays and IR waves. The rays are grouped together on one side of visible light, and the waves are grouped together on the other side. Now that we have an order we need a direction. Rays are more energetic than visible light. You can think about how long it takes for an ocean wave to pass and how quickly a sunray can hit you. This leaves only X-rays and gamma rays to having more energy than UVB.
What happens to the kinetic energy of a race car if its speed is tripled?
A) The kinetic energy increases 3 times its original value
B) The kinetic energy increases 4.5 times its original value
C) The kinetic energy increases 6 times its original value
D) The kinetic energy increases 9 times its original value
D
Kinetic energy is: KE = (1/2)mv^2. The kinetic energy is directly proportional to the square of the velocity (or speed). If the speed is multiplied by 3 (tripled), the KE must be multiplied by 3^2 = 9. Sidenote, race car spelled backwards is still race car.
An ambulance with its sirens on speeds towards you while you stand still. As the ambulance approaches (at constant velocity), you will hear a sound that:
A) Continuously decreases in pitch and intensity
B) Has a fixed pitch but increases in intensity
C) Has a fixed pitch but decreases in intensity
D) Continuously increases in pitch and intensity
B
This is a question about the Doppler effect. If the source of a sound moves towards the observer, then the perceived frequency will increase. Just like in life, the ambulance seems to get louder as it gets closer (increase intensity), but then makes much less noise after it passes. However, if the ambulance’s speed is constant, its higher pitch will remain constant as well.
A person playing croquet on a grass lawn hits his yellow ball into his opponent’s red ball. The friction coefficient between the ball and the lawn is approximately 0.25. Which of the following is true about the collision between the two balls?
A) The collision is perfectly elastic, so the red ball and yellow ball will have the same kinetic energy after collision
B) The collision is inelastic, because some energy is absorbed by the friction between the balls and the grass
C) The collision is perfectly elastic, so the yellow ball will stop moving, and transfer all momentum to the red ball
D) The collision is inelastic, and the total kinetic energy in the system will be lower after the collision
D
An elastic collision is one in which all of the kinetic energy is conserved in the collision. However, elastic collisions do not exist at large scale in the real world, and in this case the collision is not elastic. Instead, the collision is inelastic, meaning some kinetic energy is lost from the impact, usually as heat, sound, or vibration. The kinetic energy is lost as a result of the contact between the two balls, not because of the friction interaction between the grass and the ball, so answer B is not correct.
The direction of the magnetic force on a current carrying wire located in an external magnetic field is which of the following?
A) Perpendicular to the current
B) Perpendicular to the field
C) Parallel to the wire
D) A and B
D
In the situation described, there are 3 vectors and each of the 3 vectors are perpendicular to each other (you can imagine the relationship as being the x, y and z axes, or as governed by the right hand rule): the current (I), the electric field (F) and the magnetic field (B). The latter encircles the current carrying wire.
The cruising altitude of most planes is about 10,000 meters above sea level where there is less air above the plane pushing down, so the air pressure is lower (about 20 kPa outside compared to about 100 kPa atmospheric pressure at sea level). To keep everyone comfortable inside the plane, the cabin is pressurized to about 75 kPa. The passenger doors on a 747 are about 1 meter wide by 2 meters tall.
If a metric ton is 1000 kg, to pull the door open at 10,000 meters is equivalent to moving how many metric tons? (the acceleration due to gravity can be approximated as 10 m/s^2)
A) 5 x 10^-2 tons
B) 0.8 tons
C) 2 tons
D) 11 tons
D
The difference in pressure between inside and outside the cabin at 10,000 meters is:
75 – 20 = 55 kPa = 55,000 Pa or N/m^2 of pressure pushing on the door (keep in mind that the SI unit for pressure is the pascal, Pa).
Pressure is defined as force per unit area: P = F/A
The area of the door is 2 x 1 = 2m^2
So F = PA = (55,000)(2) = 110,000 N
Thus weight mg = 110,000, and since g = 10 m/s^2, then m = 11,000 kg or 11 metric tons.
A penny is thrown horizontally with an initial speed of 20 m/s. How far will it drop in 5 seconds? (Ignore air resistance).
A) 45 m
B) 65 m
C) 75 m
D) 125 m
D
The initial horizontal speed is irrelevant. Use this equation: x = (1/2)g(t)^2 = (1/2)(10)(5)^2 = 125 m.
An object of mass 3 kg floats motionless in a fluid of specific gravity 0.8. What is the magnitude of the buoyant force? (Use g = 10 m/s2).
A) 8 N
B) 16 N
C) 20 N
D) 30 N
D
Since the object is not moving, its acceleration must be zero, so the net force on it must also be zero. Therefore, the magnitude of the buoyant force upward must equal the magnitude of the weight downward, the specific gravity is extraneous information:
B = w = mg = (3 kg)(10 N/kg) = 30 N
Your significant other gave you a watch for Valentine ’s Day, and tells you it’s made of “pure gold” (density of gold = 19,000 kg/m^3). Being a mistrusting boy/girl friend, you decide to find out whether this is true. Later that day, you place the watch on a spring scale and lower it into water. The weight on the scale reads 10N out of water and 6N when completely submerged. Is the watch really made out of pure gold?
A) Yes. The watch has the same density as pure gold.
B) No. The watch’s density is only 2,500 kg/m^3
C) No. The watch’s density is only 1,000 kg/m^3
D) No. The watch’s density is only 10,000 kg/m^3
B
We should start by finding the buoyant force. In this case, it is easy, because we know the mass of the watch out of water and the mass of the watch when completely submerged. The buoyant force is of course the difference between the two (Buoyant force = “mass lost” * acceleration due to gravity). Hence, the Buoyant Force = 10N – 6N = 4N.
From this, because the buoyant force = “mass lost” *acceleration due to gravity, we can find the “mass lost” (or rather, the mass of the displaced water):
4N = mass * 10m/s^2. And so the mass of displaced water = 0.4kg
We are also told the mass of the watch outside of water (10N), so we also know the mass of the watch using the same logic:
10N = mass * 10m/s^2, and so mass watch = 1 kg
Next, in order to determine whether the watch is pure gold, we would have to find the density of the watch (so we can compare it to the density of pure gold). We know the mass of the watch (1kg), so we must now find its volume so we can solve for density using Density (p) = mass/volume. The key to solving this problem is recognizing that the displaced water and the watch both have the same volume. The density of water is common knowledge (1000 kg/m^3). (If you don’t know this, commit it to memory now! It’s important for the MCAT). Thus, using the density formula (p = m/V) we can find the Volume of water displaced:
1000 kg/m^3 = 0.4 kg/Volume. Solving for Volume gives 0.4/1000 L. This is also the Volume of the watch.
SO now we have both the mass of the watch AND the volume, and can solve for the density of the watch:
Density of watch = 1kg/(0.4/1000L) = 2,500 kg/m^3… which leads us to choose answer B. And now when we compare this density to the density of pure gold (19,000 kg/m^3), we realize your watch is NOT made of pure gold (and neither is your romance)!
Which of the following statements accurately describes the magnitude of the normal force (N) on a sled sliding down a frictionless roof that is inclined at x degrees with the horizontal?
A) N decreases as x increases, but not proportionally.
B) N is inversely proportional to x.
C) N is proportional to x.
D) N is constant, independent of x.
A
The normal force is the force that pushes up against an object. For an inclined plane, the formula for normal force is N = mgcos(x). The mass of the sled and gravity stay the same, so N must decrease as x increases due to the cosine function. Try 30 degrees for x and then 60 degrees for x in a calculator, you’ll see that the normal force decreases, but does not decrease by a factor of 2.
Santa’s sleigh slides down a snowy roof that makes an angle of 30 degrees with the horizontal. How fast is Santa accelerating?
A) 2.5 m/s^2
B) 4.9 m/s^2
C) 8.5 m/s^2
D) 9.8 m/s^2
B
The acceleration imparted by the force of gravity to an object on a frictionless inclined plane is a = g sin (theta). Therefore, if theta = 30, we find: a = gsin(theta) = 9.8sin(30) = 4.9 m/s^2.
A bar 8 meters long is placed on a pivot 2.0 meters from the lighter end of the bar. The center of gravity of the bar is located 2.0 meters from the heavier end. If a 500 N weight on the light end balances the bar, what must be the weight of the bar?
A) 125 N
B) 250 N
C) 500 N
D) 1000 N
B
The center of gravity occurs 4.0 m from the pivot point. At equilibrium:
(2.0 m)(500 N) = (4.0 m)(w)
w = ½ (500N) = 250 N
A 2.0 kg body is acted on by a 10-N force. If the body is initially at rest, what will be its velocity after 5 seconds?
A) 5.0 m/s
B) 10 m/s
C) 20 m/s
D) 25 m/s
D
F = ma a = F/m = (10 N/ 2.0kg) = 5.0 m/s^2
V = V0 + at V = at V = (5 m/s^2)(5.0 sec) = 25 m/s
Two opposite point charges (positive charge on the left and negative charge on the right) are fixed in place 5m from each other. Which one of the following is the best description of the direction of the electric field E in between the two charges?
A) E points to the left
B) E points to the right
C) E is zero
D) The direction of E depends on the sign of the test charge that is placed in the middle
B
By convention, electric field vectors always point away from positive source charges and toward negative ones. Thus, in the region between the given point charges, the electric field points to the right: away from the positive and toward the negative.
A person, of mass 70 kg, decides to do a push up. If his arms are 7/8 up the length of his body, how much force will he need to exert to accomplish one push up?
A) 200 N
B) 400 N
C) 800 N
D) 1000 N
B
To solve this problem you could use the conservation of work and find the required work to lift himself up against gravity. The distance will be the hypotenuse times the sine, soh-cah-toa.
You could also solve this problem with the understanding of torque. The person is virtually a ridged body, with the point of rotation placed at his feet. While he does this pushup he will be in rotational equilibrium. That means that if his butt moves up, his head will also move up at the same rate. With that said the torque on his weight must equal the torque he exerts.
It is interesting to note that you only lift a little bit more than half your weight when you execute a pushup.
In which situation would a person would weigh the most?
A) On the Moon
B) At the peak of Mount Everest
C) On the Earth with no air pressure
D) Keeping her volume constant but switching her density to that of helium
C
The gravitational formula tells us that her weight is essentially:
F = (GmM / r^2)
where G is the gravitational constant, M is the mass of the big body, m is the mass of the little body, and R is the distance from the two centers. Near the surface of Earth, around sea level, we approximate this as F = mg. We are allowed to obtain this approximation of g, because the small body’s mass is negligible compared to the bigger body’s mass. The remaining values are constants, and we obtain a value for g of 9.8 m/s2 . We will need to decide if each of the condition increases her weight or decreases her weight.
A) We know that the Moon has a smaller mass than Earth, so her weight will decrease. In fact her weight on the Moon is around 1/7 of that on Earth. It’s a fun number to know.
B) We increase the value of R to something above sea level. In comparison to the radius of the Earth, it’s not that much, but it is still enough to lower her weight.
C) If the Earth had no air pressure, our weight calculation is unchanged. Notice how the gravity equation has no value for air pressure or density. Every time we ‘calculate’ weight we are actually leaving off those forces.
D) Finally she would like to keep her volume but change her density to that of helium’s. We know that the density of helium is lighter than the density of air, and by extension ourselves. Let’s arbitrarily say the density of He is 0.5 the density of us. Density is just the mass over the volume. Her volume is kept constant, so her new mass is a fraction of what it initially was. This in turn will lower her weight.
Except for case C) her weight decreases in each situation. This makes her the heaviest when there is no pressure on the Earth, and even heavier when we consider it.
A small cannonball weighing 5-kg is launched vertically in the air with an initial kinetic energy of 500 joules. How high will the cannonball travel above the launch point?
A) 5 m
B) 10 m
C) 15 m
D) 20 m
B
All of the kinetic energy will be transferred into potential energy at the maximum height of the cannonball. The trick is to not replace KE with (1/2)mv2, the kinetic energy is already given! Therefore:
KE -> PE -> KE = PE -> KE = mgh -> h = KE/mg = 500 J / (5 kg)(10 N/kg) = 10 m.
When connected to a standard household voltage of 120V, a new Wii U draws 1.5A of current. How many joules per second is the Wii U using?
A) 80 J/s
B) 90 J/s
C) 120 J/s
D) 180 J/s
D
From P = IV, we get P = (1.5A)(120V) = 180 W = 180 J/s. One watt is equal to 1 joule per second. Be sure you understand units in physics!
A person stands on a scale in an elevator (true, it does not happen everyday but it is the sort of insanity that happens on the MCAT!). She notices that the scale is reading lower than her normal weight. Which of the following most reasonably describes the motion of the elevator?
A) It is moving down and slowing down
B) It is moving down at constant speed
C) It is moving up and slowing down
D) It is moving up and speeding up
C
Let’s randomly assign the upwards direction as positive. If up is positive, keeping in mind that her weight is directed down (i.e. towards the center of the Earth), the scale pushes up so that she does not go through the scale, and we know that the sum of forces is equal to ma from Newton’s 2nd Law, we get:
Fscale – weight = ma
Examine the preceding equation again keeping in mind the following interpretation: The scale reading is less than her normal weight, so ma and thus the acceleration must be negative; i.e., down. Downward acceleration means either: (1) something speeds up while moving down, or (2) something slows down while moving up (i.e. upward deceleration).
The length of the most effective transmitting antenna is equal to one-fourth the wavelength of the broadcast wave. If a radio station has an antenna 4 meters long then what is the broadcast frequency of the radio station? (the velocity of light in a vacuum is approx. 3.0 x 108 m/s)
A) 17 MHz
B) 300 MHz
C) 6.0 x 10-3 MHz
D) 15 x 10-3 MHz
A
If the antenna is 1/4 the wavelength of the broadcasting wave, then the broadcasting wave must be 4 x 4 meters = 16 meters.
The velocity of electromagnetic radiation = 3.0 x 108 m/s
Velocity = (wavelength)(frequency)
Frequency = (3.0 x 10^8)/(16) = (30 x 10^7)/(15) approximately
= 2 x 10^7 Hz = 20 x 10^6 Hz = 20 MHz approximately (Mega is the SI prefix for 10^6).
NASA sends a 100 kg astronaut to a planet with a radius three times that of Earth and a mass nine times that of Earth. The acceleration due to gravity, g, experienced by the astronaut will be:
A) Nine times the value of g on earth
B) Three times the value of g on earth
C) The same value of g as on earth
D) One third the value of g on earth
C
FG earth = G mearthmbody/r^2
On the planet we get:
FG planet = G 9mearthmbody/3r^2 = FG earth
Since the force of gravity and the mass of the astronaut remain the same on both the planet and on earth, the acceleration due to gravity must also be the same, F/m = g = constant.
An athlete runs around a 400 meter track in 60 seconds, starting and finishing at the same place. What is her speed and velocity in m/s?
A) Speed = 6.67 m/s and Velocity = zero
B) Speed = zero and Velocity = 6.67 m/s
C) Speed = 6.67 m/s and Velocity = 6.67 m/s 360deg
D) Speed = 6.67 m/s and Velocity = 6.67 m/s
A
Speed is a scalar quantity involving magnitude only: Speed = distance/time = 400/60 = 6.67 m/s. Velocity is a vector quantity involving both magnitude and direction: Velocity = displacement/time = 0/60 = zero.
Distance traveled is not dependent on a direction, but displacement is. Displacement = distance from the finish to the start, which in this case is zero as the athlete has run around an oval to arrive back at her starting place.
Assume that a pole vaulter can convert all of his kinetic energy into potential energy. If a 70.0 kg pole vaulter approaches the vault with a velocity of 9.80 m/s, about how high can he get?
A) 2.45 m
B) 4.90 m
C) 9.80 m
D) 19.6 m
B
Conservation of energy means the sum of the kinetic and potential energies must be the same at the start of the jump and at its maximum height:
1/2 mv^2 + mgh = 1/2 mv^2 + mgh
(Initial energies on the left and final energies on the right.)
There is no height initially, so there is no initial potential energy. At the top of the jump there is no velocity, so there is no final kinetic energy. This gives:
1/2 mv^2 + 0 = 0 + mgh
Therefore:
h = v^2 / 2g = (9.8 m/s)^2 / 2(9.8 m/s^2) = 4.9 m
The mass of the vaulter cancels out.
A construction worker accidentally pushes a 100kg block of metal alloy off a 8 meter high stand. The block lands on top of a stake partially put into the ground, driving it completely into the dirt.
What is the velocity of the block just before striking the stake? Ignore air resistance.
A) 9.80 m/s
B) 2.00 m/s
C) 12.5 m/s
D) 16.0 m/s
C
Vf^2 = Vi^2 + 2ax = sqrt[0 + 2 (9.8 m/s2)(8 m)]
V = 12.5 m/s
A ball is thrown vertically upward with an initial velocity of 40.0 meters per second. What will be its velocity after 2.00 seconds?
A) 20.4 m/s
B) 9.80 m/s
C) 49.0 m/s
D) 80.0 m/s
A
v = v(0) + at. Here is a quick tip to speed up a question like this on the exam. Estimate the acceleration due to gravity using a = -g = -9.8 m/s^2 ~ -10 m/s^2. The velocity is approximately:
v = v(0) + at v = 40 m/s – 10 m/s^2 (2 s)
v = 40 m/s – 20 m/s = 20 m/s
The closest answer to 20 m/s is A.
What is the current in a 60-W light bulb operating at 120-V household voltage?
A) 2.0 A
B) 1.5 A
C) 1.0 A
D) 0.5 A
D
60 W represents the power usage of the bulb. Power is the product of current and voltage. Thus:
P = IV
I = P / V = 60 W / 120 V = 0.5 A
A cruise missile is fired at an angle with the horizontal. The air resistance is negligible. The initial horizontal velocity component is twice that of the initial vertical velocity component. The trajectory of the cruise missile is best described as:
A) Semicircular
B) Translational
C) Parabolic
D) Hyperbolic
C
If air resistance is neglected, the trajectories of all projectiles fired near the surface of the earth follow a parabolic path because the horizontal velocity is constant while the vertical acceleration is also constant.
Which of the following statements regarding electric current is true?
A) Electric current will only flow from a higher potential to a lower potential
B) Electric current will only flow from a lower potential to a higher potential
C) Oscillate between potentials of higher and lower energy
D) Remain in equilibrium
A
Electric current moves in the direction positive charges move in. Therefore, the electric flow of current flows from the point of higher potential to lower potential, similar to how water falls from the top of the waterfall to the bottom.
A force of 1 minion can cause 1 gram to accelerate at 1 cm/s2. How many newtons are equivalent to 1 minion?
A) 10^-5
B) 10^-1
C) 10^1
D) 10^5
A
1 newton = 1 kgm/s^2
Therefore:
1 (gcm)/s^2 = x (kg*m)/s^2 -> 1(10^-3kg)(10^-2m) = 10^-5
A ball with a mass of 1.0 kg sits at the top of a 30degrees incline plane that is 20.0 meters long. If the potential energy of the ball is 98 J at the top of the incline, what is the potential energy once it rolls half way down the incline?
A) 0 J
B) 49 J
C) 98 J
D) 196 J
B
Since the height is decreasing, the Ep is decreasing and must have a value less than its initial reading 98 J. D is eliminated because its value is higher than the initial Ep value. C is eliminated because its value is the same as the initial value of the Ep. A is eliminated because the only way to have zero Ep is if the body is at ground level. That leaves B as the only option.
A horse accelerates uniformly from 0 to 20 mi/h in 2 seconds. What is the acceleration?
A) 10 mih^-1
B) 10 mi^-2
C) 10 mih^-1s^-1
D) 10 mi*h^-2
C
The formula for acceleration is velocity divided by time:
a = v/t = ((20-0) mi/h) / 2 s = 10 mih^-1s^-1
A construction worker uses a crane to vertically lift an object weighing 2000 N to the top of a platform at a constant rate. If it takes 30 seconds to lift the object 150 meters, what is the rate of energy consumed by the motor in the crane?
A) 5.0 kW
B) 8.0 kW
C) 10.0 kW
D) 12.0 kW
C
We can use the equation Power = Force*velocity to solve this problem. The object moves 150 meters in 30 seconds, so the velocity must be (150m/30s) = 5 m/s. Plugging this back into the original equation of P = Fv, then P = (2000 N)(5 m/s) = 10 kW.
Which expression gives the acceleration of a 1kg mass on a frictionless inclined plane at 30degrees to the horizon, given that g = 9.8 m/s^2?
A) a = 9.8 m/s^2
B) a = cos 30o x 9.8 m/s^2 = 8.5 m/s^2
C) a = sin 30o x 9.8 m/s^2 = 4.9 m/s^2
D) a = tan 30o x 9.8 m/s^2 = 5.7 m/s^2
C
Gravity is calculated from the vertical component of the force on the mass: sin theta = opposite/hypotenuse.
Consider the following diagram which reveals a positive test charge that is located between two charged spheres, X and Y. Sphere X has a charge of +3Q and is located 0.6 meters from the test charge. Sphere Y has a charge of -3Q and is located 0.3 meters from the test charge.
If the magnitude of the force on the test charge due to sphere X is F, what is the magnitude of the force on the test charge due to sphere Y?
A) 4F
B) F/4
C) 2F
D) F/2
A
Keeping Coulomb’s law in mind, if you reduce the distance by 1/2, then the force increases by the inverse squared of 1/2 which is 4 times. Note the question is only asking about the magnitude of the forces as opposed to their directions. If the direction were asked, then the sign of the charge (i.e. positive or negative) would matter.
Three metal spheres X, Y and Z, are identical in size but carry differing electric charges of –Q, +2Q and -3Q, respectively. The first metal sphere X is brought into contact only with the sphere Y, and then X is brought into contact only with sphere Z. After X makes contact with spheres Y and Z, in the order described, the charge on sphere X is most consistent with which of the following?
A) -5/4Q
B) -2Q
C) -Q
D) -Q/2
A
The basic principle: the spheres are equal in size so when they touch (conduction of charge), the charge will be split equally between the 2 spheres (this is consistent with the Conservation of Charge). When the spheres are separated, each sphere will retain 1/2 of the charge (because they are identical in size).
1) X plus Y: When -Q touches +2Q, the overall charge of the 2 spheres would be -Q + 2Q = +Q but that charge is shared with 2 spheres so each sphere has a +1/2Q charge.
2) new X plus Z: Now +1/2 Q – 3Q = -5/2Q and half of this is -5/4Q.
Two objects are in motion, one has 1/2 the velocity of the other but twice the mass. External forces bring each mass to rest. Choose the correct statement.
A) Twice as much work is done on the smaller mass
B) Twice as much work is done on the larger mass
C) The same amount of work is done on both masses
D) The work cannot be determined without knowing the displacement
A
Simple way:
Use the Work-Energy Theorem where the variation of the kinetic energy of a system is equal to the work of the net force applied to the system. Thus the work is just the change in kinetic energy (i.e. final MINUS initial). But the final is 0 because the final velocity is 0 (at “rest”). So we get:
Work = -m(v^2)/2
Looking at the equation, it is clear that doubling the velocity has a greater impact on the work as compared to doubling the mass.
Side Note: Friction always does negative work because it is opposite to the direction of motion. Similarly, work must be negative in this problem.
Alternate method:
Work = Force times distance (actually, displacement) = m (a) x
To determine the acceleration a (actually, the deceleration):
V^2 = Vo^2 + 2ax = 0 (each object has a final vel. of 0)
a = – (Vo^2)/2x
Work = m [- (Vo^2)/2x] x = -m(Vo^2)/2
Now by testing the numbers given, you can see that the original velocity has a greater impact than the mass.
An increase in the motion of molecules of a gas confined in a metal tank will be observed as an increase in:
A) The pressure of the gas only
B) The temperature of the gas only
C) The temperature of the gas and a decrease in its pressure
D) Both the temperature and pressure of the gas
D
The word “kinetic” means movement or motion. An increase in motion means that there is an increase in kinetic energy which we know is directly related to temperature (CHM 4.1.2). When there is an increase in motion, that means there is an increase in the force of the molecules hitting the walls of the container. Pressure is force per unit area (PHY 6.1.2) so the pressure must increase if the motion increases.
A block of wood is held half immersed in the water. When released, it submerged to a greater degree but remained afloat. When the block was initially released, which of the following must have been true?
A) Weight of fluid displaced > weight of block
B) Density of fluid < density of block
C) Initial buoyant force < maximum buoyant force
D) Maximum buoyant force = half the weight of the block
C
Tricky! You must recognize that the half immersed block would submerge as long as its density is greater than 1/2 the density of water or a specific gravity of 0.5. Thus this block may: (i) have a specific gravity between 0.5 and 1.0 (which means the block’s density would be less than that of water); or (ii) it could have a density equal to that of water; but (iii) it could NOT have a density greater than that of water (this would make it sink to the bottom but the question says that it remains afloat so (iii) is not possible): nonetheless, it would submerge from a position of being held half immersed [thus answer choice B. is not the best answer because of the preceding points (i) and (ii)]. When the block sinks, it will certainly displace more water than it did initially; therefore, the buoyant force increases to its maximum.
All of the following quantities are vectors EXCEPT one. Which one is the EXCEPTION?
A) Electric current
B) Magnetic field
C) Electric force
D) Electric potential
D
Fields are vectors because they cause forces, and force is a vector. Current is a vector because charge can flow in either direction in a wire. However, electric potential is related to potential energy (PE = qV), and all forms of energy are scalar quantities.
Which of Newton’s Laws of Motion is best described as “For every action there is an equal and opposite reaction.”?
A) Newton’s First Law of Motion
B) Newton’s Second Law of Motion
C) Newton’s Third Law of Motion
D) Newton’s Fourth Law of Motion
C
Newton’s Third Law of Motion states that: “When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.”
Newton’s First Law of Motion deals with unbalanced forces or inertia and his second law with force, mass and acceleration, F = ma.
Note: Newton only had three Laws of Motion.
A patient in a wheelchair notices his wheels are sometimes warm after he travels. If the patient traverses the same distance across the same material surface, which situation would his wheels be the hottest after completion?
A) Rolling down an incline
B) Rolling up an incline
C) Rolling backwards on an even floor
D) Going around in a circle, on a banked curve
C
Friction is the cause of the heated wheels. The heat energy produce by friction is the work done by frictional forces.
Because the distance and the surfaces are the same, all we need to focus on is the normal force. Normal force is the equal but opposite force a body, generally it’s weight, applies to the contacting surface. On any incline only a fraction of the weight, Wa, is applied to the inclined surface. Assuming the acceleration of his rolls is not directly into the ramp, you will have the greatest friction on a flat surface. This is apparent when we tend to see objects sliding on ramps and not as much on the floor.
A 1 kg gold ball is thrown straight down from a height of 1m onto a horizontal floor and bounces up. It’s speed at release is 4 m/s. The speed before just after impact is 10 m/s. Determine the magnitude of the impulse delivered to the floor by the gold ball.
A) 16 N-s
B) 8 N-s
C) 4 N-s
D) 12 N-s
A
This question combines two principles, translational motion and impulse. The magnitude of impulse is given by the equation
J = Ft = m(vf-vi)
In this case, we are not given time (t) so to find the magnitude of impulse, we must focus on the change in momentum. The change in momentum is given with the equation
m(vf – vi) = 1 kg * (10 m/s – vi)
vf is the velocity directly after impact with the floor. vi is velocity directly before impact. It is important to note that vi is also the final velocity of the ball in the reference frame of throwing the ball to the ground. Thus,
vf2 = vi2 +2a?x = 42 + 2(10)(1) = 36
Our velocity right before impact is thus 6 m/s. Because velocity is a vector function, we must remember that this velocity is in the opposite direction of vf. Finally, we return to our previous impulse equation substituting
-6 m/s for vi and we see that the magnitude of impulse (J) is 16 N-s.
An air hockey puck slides on a surface of a frictionless table. If the mass of the puck is 250 grams, and it moves in a straight line with a constant velocity of 4 m/s, find the net force acting on the puck.
A) 0 N
B) 1 N
C) 62.5 N
D) 1000 N
A
Since the velocity is constant, the acceleration a is zero, so using F = ma, we know that the net force must be zero as well.
An electric generator produces electricity by an alternating current with a frequency of 50 cycles per second. If the rms voltage is 100 V, what is the approximate maximum potential difference produced by the generator?
A) 50 V
B) 71 V
C) 141 V
D) 200 V
C
By definition, Vrms = Vmax / sqrt(2). Therefore, Vmax = sqrt(2)*Vrms = (1.41)(100V) = 141 V.
What is the work done in holding a 20-N weight at a height of 2 m above the floor for a total of 5 s?
A) 0 J
B) 2 J
C) 8 J
D) 200 J
A
Work is force times distance moved. A body held at a given height is not in motion, so work is no longer being performed on it.
Two point charges attract each other with a force of 3.6 x 10-6 N when they are 3 m apart. What is the force if the distance is increased to 6 m?
A) It is tripled
B) It is reduced to one-ninth
C) It is quadrupled
D) It is quartered
D
The force is inversely proportional to the square of the distance between the point charges. Since the distance is doubled, the force must be quartered.
What is the half-life of a radionuclide if 1/16 of its initial mass is present after 2 hours?
A) 15 min
B) 30 min
C) 45 min
D) 60 min
B
In every half-life, the mass decreases to half its previous value:
1/16 = 1/2^4
It takes four half-lives to decay down to 1/16 the original mass. Each must be 30 minutes long since the entire process takes two hours.
A 70 kg construction worker accidentally pushes a 100kg block of metal alloy off a 8 meter high stand. The block lands on top of a stake partially put into the ground, driving it completely into the dirt.
What is the kinetic energy of the block just before striking the stake? (The previous question revealed the final velocity of the block was 12.5 m/s.)
A) 3263 J
B) 7840 J
C) 8500 J
D) 12,000 J
B
E = (1/2)mv2 = (1/2) (100kg) (12.5 m/s)2 E = 7840 J
Monochromatic light passes through two parallel slits in a screen and falls on a piece of film. The pattern produced is an example of:
A) Interference and reflection
B) Interference and diffraction
C) Refraction and diffraction
D) Diffraction and polarization
B
The light passing through each slit is diffracted (bent), and the two resulting beams overlap on the film to form interference patterns.
Force must be applied to initiate motion for an object in:
A) Earth’s atmosphere
B) Outer space
C) The ocean
D) All of the above
D
All of the choices are indicative of Newton’s First Law of Motion. An object at rest will remain at rest unless a force is acted upon the resting object. Every location in the answer choice will remain still even in space, unless force is applied.
The inertia that an object possesses depends on its:
A) Velocity
B) Mass
C) Volume
D) None of the above
B
Mass is essentially a quantitative measure of an object’s inertia. The capacity of an object to resist changes in motion; more mass = more inertia. Inertia is proportional to the mass of the object; more mass means more force is required to start or stop moving.
