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MCAT Physics > Translational Motion > Flashcards

Flashcards in Translational Motion Deck (33)
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1
Q

What SI unit and common variables are associated with length?

A

Length ,or distance, has SI units of meters (m).

The variable d and x are used for distance, while h is used for height, z for depth, and r for radius.

2
Q

What SI unit and common variables are associated with time?

A

Time has SI units of seconds (s).

The variable t is used for time; T is used for period and also has SI units of seconds.

3
Q

What SI unit and common variables are associated with area?

A

Area has SI units of meters2 (m2).

The variable A is used for area, while S is used for surface area.

4
Q

What SI unit and common variables are associated with volume?

A

Volume has SI units of meters3 (m3).

The variable V is used for volume.

5
Q

What SI unit and common variables are associated with velocity?

A

Velocity has SI units of meters/seconds (m/s).

The variable v is used for velocity (a vector). Note that m/s are also used to measure speed (a scalar).

6
Q

What SI unit and common variables are associated with acceleration?

A

Acceleration has SI units of meters/seconds2 (m/s2).

The variable a is used for acceleration (a vector).

7
Q

What two characteristics are necessary to define a vector?

A

Magnitude and direction

Displacement, velocity, and acceleration are vector quantities.

8
Q

What is the difference between distance and displacement?

A

Distance is a scalar, while displacement is a vector.

Distance includes only magnitude, not direction; it is equal to the number of total meters traveled. Displacement includes both magnitude and direction and is equal to the number of meters between the starting and ending points.

9
Q

What is the difference between speed and velocity?

A

Speed is a scalar, while velocity is a vector.

Speed includes only magnitude, not direction; velocity includes both magnitude and direction. Velocity can have a negative sign, while speed is always positive.

10
Q

What is the magnitude of a vector?

A

Magnitude is the quantity, size, or amount of a measurement. Magnitude alone is a scalar value, since it lacks direction.

11
Q

What is the direction of a vector?

A

Direction is a piece of information that provides spacial orientation, angle, or path.

By convention, right and up (two perpendicular directions) are fixed as positive, while their opposites (left and down) are negative.

12
Q

What is the magnitude of a velocity vector that points directly down at 5 m/s?

A

5 m/s.

Magnitude is the quantity, size, or amount.

13
Q

What is the direction of a velocity vector that points directly up at 13 m/s?

A

Directly upwards.

Direction is the angle, orientation, or path.

14
Q

Describe the general process for vector addition.

A

Vectors are added “tip to tail,” forming a continuous pathway from the first arrow to the last one.

The sum, or resultant, vector is made by connecting the original tail to the final tip.

15
Q

Describe the general process for vector subtraction.

A

Vectors are subtracted in the same process as addition: “tip to tail”. The direction of the vector being subtracted must be reversed prior to adding them.

16
Q

Define:

component vectors

A

Component vectors represent the magnitudes of a given vector along the x axis and y axis.

Generally, these are referred to as the “x component” and the “y component.” In the image below, vector A is shown with its x and y components as Ax and Ay, respectively.

17
Q

Give the formula for the x component of a force in the xy plane.

A

Fx = Ftotal cos θ

In general, [vector]x = [original vector] * cos θ.

18
Q

What is the x component of velocity for a ball thrown upwards at 4 m/s, 30º to the horizon?
Note that sin(30º) = 0.5 and cos(30º) = 0.86.

A

3.4 m/s

vx = 4 cos (30º) = 4 (.86) = 3.4 m/s

19
Q

Give the formula for the y component of a force in the xy plane.

A

Fy = Ftotal sin θ

In general, y vector = original vector * sin θ.

20
Q

What is the y component of velocity for a ball thrown upwards at 4 m/s, 30º to the horizon?
Note that sin(30º) = 0.5 and cos(30º) = 0.86.

A

2 m/s

vy = 4 sin (30º) = 4 (.5) = 2 m/s

21
Q

What formula relates displacement, time, and acceleration?

A

Δx = v0t + 1/2 at2

When dealing with an object that starts at rest, v0 is equal to zero and the first term can be canceled out. When dealing with cases of zero acceleration, as for horizontal velocity with no air resistance, the second term can be canceled out.

22
Q

Define:

instantaneous velocity

A

Instantaneous velocity is the direction and magnitude of the rate of change of distance per unit time.

v = Δx / t

23
Q

Give the instantaneous velocity for a 3 kg block with a momentum of 12 kg*m/s.

A

4 m/s

Momentum is equal to velocity times mass; in variables, p = mv. Here, 12 = (3)(v), so v must be equal to 4 m/s.

24
Q

Define:

average velocity (vave)

A

Average velocity is the total displacement and direction traveled from an initial position, divided by the total time.

vave = Δxtotal / Δttotal

or vave = (vf + vi)/2

Note that the second equation assumes constant acceleration, which is also assumed on the MCAT unless specified otherwise.

25
Q

Give the average velocity for a 1 kg block after it falls from rest for 2 seconds.

A

9.8 m/s

v = (1/2) at2

vf = (1/2) (9.8) (2)2 = 2 (9.8) = 19.6 m/s

vi = 0 (given as “rest”)

vave = (vf + vi) / 2

vave = (19.6 + 0) / 2 = 9.8 m/s

26
Q

What formula(s) can be used to find final velocity when given initial velocity?

A

vf = vi + at

or vf2 = vi2 + 2aΔx

Where:

vf = final velocity (m/s)
vi = initial velocity (m/s)
a = acceleration (m/s2)
Δx = displacement (m)
t = time (s)

27
Q

Give the velocity of a 1 kg block after it falls from rest for 2 seconds.

A

19.6 m/s

vf = vi + at

vf = 0 + (9.8)(2) = 2(9.8)
19.6 m/s

28
Q

Define:

acceleration

A

Acceleration is the rate at which velocity changes per unit of time.

a = Δv / t or a = Δx / t2

29
Q

What change must have been made to acceleration if the same distance can now be traveled in half the time?

A

The acceleration must have been multiplied by 4.

Since a is proportional to Δx / t2, halving t quadruples a.

30
Q

What is the acceleration that is always associated with an object in free fall?

A

9.8 m/s2

This is the acceleration due to gravity, commonly called g. On the MCAT, any falling object is assumed to be in free fall (no air resistance) unless told otherwise.

Note that while it’s convenient to use 10 m/s2 for calculations, the MCAT expects you to still choose the correct answer mathematically.

31
Q

How can the maximum height of a moving projectile be found?

A

The maximum height of a projectile can be found by finding the point where the vertical component of velocity, vy, equals zero.

The object moves upwards until it reaches this point, and afterwards is accelerated downwards by gravity. If the projectile arc is symmetric, this position occurs after half of the total time in flight has elapsed.

32
Q

What is the maximum height of a ball thrown directly upwards from the ground with a velocity of 10 m/s?

A

The ball’s maximum height is 5m.

The kinematics equation that most easily solves this question is:

vf2 = v02 + 2aΔx

Set vf equal to 0 m/s to represent the velocity at the maximum height. v0 = 10 m/s, and a = -10m/s2.

0 = 100 + 2(-10)Δx
Δx = 5m

33
Q

Define:

air resistance

A

Air resistance is the frictional force that opposes an object moving in free fall.

Fair = -kv2

The force of air resistance is proportional to the square of the velocity of the object falling. The constant k is a function of the object’s shape and surface area. Note that you do not need to memorize this equation, but be aware of the presence or absence of air resistance in every projectile motion problem.