AP Physics C: Mechanics 4.3 Conservation of Linear Momentum Questions

Analyse isolated-system interactions by conserving vector momentum across collisions, recoil and explosions, including two-dimensional components, staged motion, and data.

Exam points

define a system whose external impulse is negligible over the interaction interval
conserve signed momentum in one-dimensional collisions, sticking events, recoil, or explosions
conserve perpendicular momentum components in a two-dimensional interaction
use center-of-mass motion as a check on the conserved momentum of an isolated system
combine momentum conservation with energy, projectile, swing, or circular-motion stages

Covered syllabus points

4.3.A—Describe the behavior of a system using conservation of linear momentum 4.3.B—Describe how the selection of a system determines whether the momentum of that system changes

[Maximum number: 3]

Two blocks, 1 and 2, slide toward each other on a horizontal surface. Block 1 has mass m and slides in the +x-direction with constant speed $2 v_{0}$ . Block 2 has mass 6 m and slides in the -x-direction with constant speed $v_{0}$ , as shown in Figure 1. The blocks then collide and stick together. The collision occurs from time t=0 to $t=t_{c}$ . After the collision, where $t>t_{c}$ , the blocks move together with the same constant speed.

Figure 1

Consider a new scenario where Block 1 initially slides in the +x-direction with a new constant speed $v_{1}$ and Block 2 again initially slides in the -x-direction with constant speed $v_{0}$ .

The blocks collide and stick together. In this new scenario, the two-block system has constant speed $v_{0}$ after the collision.

Derive an expression for $v_{1}$ in terms of $v_{0}$ . Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

B	For a multistep derivation that includes conservation of momentum	Point B1
		For indicating that the magnitude of the final momentum of the two-block system is $7 m v_{0}$	Point B2
		For a correct expression for $v_{1}$ in terms of $v_{0}$	Point B3
		Example Response $\begin{aligned} & \sum \vec{p}_{0}=\sum \vec{p}_{f} & m v_{1}+6 m\left(-v_{0}\right)=7 m\left(v_{0}\right) & m v_{1}=13 m v_{0} & v_{1}=13 v_{0} \end{aligned}$

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Covered syllabus points

Question 1