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.
