AP Physics 1 Unit 2: Force and Translational Dynamics

Explain translational motion through system models, force diagrams, Newton’s laws, gravitational and contact forces, springs, and circular motion.

Covered syllabus points

2.1 Systems and Center of Mass 2.2 Forces and Free-Body Diagrams 2.3 Newton’s Third Law 2.4 Newton’s First Law 2.5 Newton’s Second Law 2.6 Gravitational Force 2.7 Kinetic and Static Friction 2.8 Spring Forces 2.9 Circular Motion

[Maximum number: 3]

(12 points, suggested time 25 minutes)

(a)

The students calculate the value of $g_{\text {exp }}$ to be significantly lower than the accepted value of $9.8 \mathrm{~m} / \mathrm{s}^{2}$ .

[ 3 ]

(i)

What is a physical reason, other than friction or air resistance, that could lead to a significant difference in the experimentally determined value of $g_{\text {exp }}$ ?

[ 1 ]

(ii)

Briefly explain how the physical reason you identified in part (c)(i) would lead to the decrease in the experimentally determined value of $g_{\text {exp }}$ .

Figure for Question (ii) — AP Physics 1: Algebra-Based

The students want to confirm that the acceleration is the same whether the cart rolls up or down the ramp. The students start the cart at the bottom and give the cart a quick push so that it rolls up the ramp and momentarily comes to rest. The x-axis is still defined to be parallel to the ramp with the origin at the top.

[ 2 ]

For correctly indicating the functional dependence between the reason listed in part (c)(i) and $g_{\text {exp }}$

Accept one of the following:

- Correctly indicating the functional dependence between the physical factor in the materials used and $g_{\text {exp }}$ (e.g., if the rotational inertia of the rotating wheels is nonnegligible, the cart will have a smaller acceleration and $g_{\text {exp }}$ will be smaller.)

- Correctly indicating the functional dependence between the physical factor in the environment and $g_{\text {exp }}$ (e.g., if the experiment was performed at a high elevation, the acceleration will be smaller and $g_{\text {exp }}$ will be smaller.)

- Correctly indicating the functional dependence between the physical error in the measurement collection and $g_{\text {exp }}$ (e.g., if the angle of the ramp is smaller than the measured value, the cart will have a smaller acceleration and $g_{\text {exp }}$ will be smaller.)

Example Response

The expression I derived for the value for $g_{\text {exp }}$ did not take into consideration that the wheels had any rotational inertia. If the wheels have rotational inertia and are rotating, the acceleration of the cart would be less than $g \sin \theta$ , so the value of $g_{\text {exp }}$ would be less than $9.8 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}$ .

Total for part (c) 2 points

[Maximum number: 4]

Figure for Question 2 Force and Translational Dynamics question 2 — AP Physics 1: Algebra-Based

(12 points, suggested time 25 minutes) A student in a physics lab has a block with a fan attached to it, as shown in the figure above. The fan has a pivot so that the angle $\theta$ it makes with the horizontal can be adjusted between 0° and 90°. When the fan is pointed horizontally so that $\theta=0^{\circ}$ , the block accelerates from rest along a track, even though there is friction between the block and the track. For the following questions, assume that the student has access to equipment that would usually be found in a school physics laboratory.

(a)

Figure for Question (a) — AP Physics 1: Algebra-Based

(a) Describe an experimental procedure that the student could use to measure the force F that the air exerts on the fan-block system when the fan is turned on. Assume that the magnitude of this force is the same for all angles $\theta$ .

[ 3 ]

(i)

Figure for Question (i) — AP Physics 1: Algebra-Based

i. What quantities would be measured?

(ii)

ii. What equipment would be used for the measurements, and how would that equipment be used? Include a labeled diagram of the experimental setup.

(iii)

Figure for Question (iii) — AP Physics 1: Algebra-Based

iii. Describe the overall procedure to be used. Give enough detail so that another student could replicate the experiment.

(iv)

Figure for Question (iv) — AP Physics 1: Algebra-Based

iv. Describe how the force can be determined from the measurements described in parts (a)i-iii.

(b)

Figure for Question (b) — AP Physics 1: Algebra-Based

(b) Describe an experimental procedure that would allow the student to use the fan-block system, with the fan turned on, to find the coefficient of kinetic friction between the block and the track.

[ 3 ]

(i)

iv. On the dot to the right, which represents the fan-block system, draw and label the forces (not components) that are exerted on the system during the experiment described in parts (b)i-iii. Represent each force by a distinct arrow starting on, and pointing away from, the dot.

(c)

Figure for Question (c) — AP Physics 1: Algebra-Based

(c) Describe how to analyze the data from the experiment described in parts (b)i-iii in order to determine the coefficient of kinetic friction between the block and the track. Your analysis may include the force F exerted by the air on the fan-block system. Do not add to the free-body diagram in part (b)iv.

[ 4 ]

For using kinematic data to obtain acceleration, a, or showing that a=0

Alternatively the point can be earned using the Work-Energy solution with kinetic

energy $K=(1 / 2) m v^{2}$

For relating frictional force and coefficient of kinetic friction as $F_{f}=\mu_{K} F_{N}$

For a correct representation of the normal force, correctly referring back to a

measurement of the fan-block system

$F_{N}=m g$ if $\theta=0$ or $F_{N}=m g+F \sin \theta$ if $\theta \neq 0$

For using Newton's second law, consistently with normal force above, for the

appropriate forces or force components in the direction of the fan's motion that

would lead to the determination of the coefficient of kinetic friction

$F_{\text {net }}=m a$

$F-F_{f}=m a$

$\mu_{k}=\frac{F-m a}{m g}$ if $\theta=0$ or $\mu_{k}=\frac{F \cos \theta-m a}{m g+F \sin \theta}$ if $\theta \neq 0$

Alternatively the point can be earned using the Work-Energy solution that would lead

to the determination of the coefficient of kinetic friction.

Example 3 (continued from above): $\theta=0$ Determine the slope of each v vs. t graph,

to get the acceleration for each trial, and average the accelerations. Call this average

acceleration a. The kinetic frictional force exerted by track on block is

$F_{f}=\mu F_{n}=\mu m g$ , where m is the mass of the fan-block as found in part (a), since

the acceleration is purely horizontal and hence $F_{n}$ and m g must balance. So, by

Newton's second law, letting F denote the force exerted by the air on the fan found

in part (a), we get

Solve for $\mu$ to get $\mu=\frac{F-m a}{m g}$

Example 4 (continued from above): $\theta=0$ Let d denote distance from block to second

photogate and t denote the corresponding time. Since $v_{0}=0, d=\frac{1}{2} a t^{2}$ and

hence $a=\frac{2 d}{t^{2}}$ . For each trial, calculate that acceleration, and take the average,

which becomes our best estimate of a. [Rest of solution is as in example 3]

[Maximum number: 1]

Consider the situation in which your hand is pushing a book across a rough desktop with lots of friction. Of the many forces involved, consider only these two individual forces: the force on your hand from the book and the force the book is experiencing from your hand. While the book is accelerating from rest to its final velocity, which statement best compares the force experienced by your hand compared with that experienced by the book?

Force on book > force on hand

Force on hand > force on book

Force on hand = force on book

The relationship between these two forces depends on the frictional force.

[Maximum number: 1]

Three identical blocks, A, B, and C, slide on three dif ferent rough ramps, 1, 2, and 3, respectively. Ramp 3 is steeper than Ramp 2, which is steeper than Ramp 1, as shown. The blocks slide with constant velocities. Which block, if any, experiences the greatest net force?

Block A

Block B

Block C

All blocks experience the same net force.

Figure for Question 2 Force and Translational Dynamics question 4 — AP Physics 1: Algebra-Based

All question bank results loaded

Covered syllabus points

2 Force and Translational Dynamics question 1

Question (a)

Question (i)

Question (ii)

2 Force and Translational Dynamics question 2

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (iv)

Question (b)

Question (i)

Question (c)

2 Force and Translational Dynamics question 3

2 Force and Translational Dynamics question 4