AP Physics 1 4.3 Linear Momentum Conservation Overview

Analyze collections of objects as systems and apply momentum conservation when external forces do not transfer net momentum.

[Maximum number: 7]

A student has a cart of mass $m_{\mathrm{c}}$ and a block of mass $\frac{1}{5} m_{\mathrm{c}}$ , as shown in Figure 1.

- At time t=0, the cart is moving to the right across a horizontal surface with constant

speed $v_{\mathrm{c}}$ , and the student releases the block from rest.

- At $t=t_{1}$ , the block collides with and sticks to the top of the cart. The block does not slide

on the cart.

- At $t=t_{2}$ , the block-cart system continues to move to the right with constant speed $v_{f}$ .

Figure 1

(a)

A.

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(i)

On the axes shown in Figure 2, sketch a graph of the magnitude $p_{x}$ of the x-component

of the momentum of the block-cart system as a function of time t from t=0 until $t>t_{2}$ .

Figure 2

[ 2 ]

A (i) For sketching one of the following:

- A constant $p_{x}$ for $t<t_{1}$

- A constant $p_{x}$ for $t>t_{1}$

For sketching a line that demonstrates momentum is constant

Point A2

Accept one of the following:

- A continuous, nonzero, horizontal line from t=0 to $t=t_{2}$

- A continuous, nonzero, horizontal line from t=0 to $t>t_{2}$

Example Response

Official scoring-guideline example response

(ii)

Derive an expression for the speed $v_{f}$ of the block-cart system after time $t=t_{2}$ in terms

of $m_{\mathrm{c}}, v_{\mathrm{c}}$ , and physical constants, as appropriate. Begin your derivation by writing a

fundamental physics principle or an equation from the reference information.

[ 2 ]

(ii) For including a conservation of momentum equation

Point A3

Scoring Note: Part A (ii) and part A (iii) may be scored together, if necessary.

For setting $m_{\mathrm{c}} v_{\mathrm{c}}$ equal to the momentum of the block-cart system after the collision

Point A4

Scoring Note: A correct, isolated, final expression of $v_{f}=\frac{5}{6} v_{\mathrm{c}}$ earns points A3 and

A4.

Example Response

$\begin{aligned} & p_{i}=p_{f} \\ & m_{\mathrm{c}} v_{\mathrm{c}}=\left(m_{\mathrm{c}}+m_{\mathrm{b}}\right) v_{f}=\left(m_{\mathrm{c}}+\frac{1}{5} m_{\mathrm{c}}\right) v_{f} \\ & v_{f}=\frac{5}{6} v_{\mathrm{c}} \end{aligned}$

(b)

Consider the case where a new block is dropped and collides with the top of the cart. The

new block slides along the cart during the collision but does not slide off the cart. The time

interval from when the new block collides with the cart and moves together with the cart

is $\Delta t$ . During $\Delta t$ there is a frictional force between the new block and the cart.

Indicate whether the x-component of the momentum of the new block-cart system increases,

decreases, or remains constant during $\Delta t$ .

Increases

Decreases

Remains constant

Justify your response.

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AP Physics 1 4.3 Linear Momentum Conservation Overview

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4.3 Conservation of Linear Momentum question 1

Question (a)

Question (i)

Question (ii)

Question (b)