Unit 4: Linear Momentum
Physics C: Mech · Unit 4 · Paper 1

Linear Momentum unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Each paper is built from this unit’s 42 terms and is the same for everyone, so a teacher can assign “Unit 4, Paper 1” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 37 min 34 points0/17 attempted
1

Perfectly elastic collision

2

Equal-mass elastic collision

3

The impulse–momentum theorem

4

Center of mass

5

Two-dimensional collisions

6

Center of mass position

7

Momentum and impulse as integrals

8

Kinetic energy in the center-of-mass frame

9

Ballistic pendulum sequence

10

Thrust

11

The center-of-mass frame

12

Perfectly inelastic collision

Short answer 1. Define or explain: Elastic collision in one dimension

3 pts

Short answer 2. Define or explain: Elastic collision special cases

3 pts

Short answer 3. Define or explain: Impulse as area under a force–time graph

3 pts

Short answer 4. Define or explain: Variable-mass systems

3 pts

Free response

10 pts

MATHEMATICAL ROUTINES (Question 1, 10 points). Two blocks slide toward each other on a horizontal surface. Block 1 has mass m and slides in the +x-direction with constant speed 2v0. Block 2 has mass 6m and slides in the −x-direction with constant speed v0 (Figure 1). The blocks collide from t = 0 to t = tc, stick together, and afterward move with the same constant speed. (Figure 2 gives momentum-vector grids; the arrow for Block 1 before the collision is drawn — 2 units to the right.)

A(i). Describe the momentum arrows on the grids for Block 2 before the collision and for the two-block system before and after the collision (arrows start at the zero-momentum line, lengths proportional to magnitude, zero drawn as a dot).

A(ii). During 0 ≤ t ≤ tc, the force on Block 2 from Block 1 along the x-direction is modeled by F(t) = Fmax·sin(At), where A is a positive constant. Derive an expression for Fmax in terms of m, v0, A, tc, and physical constants, as appropriate.

B. In a new scenario, Block 1 initially slides in the −x-direction with speed v1 and Block 2 initially slides in the +x-direction with speed v0. The blocks collide and stick, and the two-block system afterward has constant speed v0. Derive an expression for v1 in terms of v0.