AP Physics C Mechanics 4.3: Conservation of Linear Momentum

Analyze collections of objects as systems and apply momentum conservation when external force or impulse does not change total momentum.

[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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