Physics C: Mech · Unit 4 · Paper 3

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.

Paper 1 Paper 2 Paper 3

Each paper is built from this unit’s 42 terms and is the same for everyone, so a teacher can assign “Unit 4, Paper 3” 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 40 min 36 points0/17 attempted

Impulse-momentum in two dimensions

Center of mass of a continuous body

Impulse as area under a force–time graph

Momentum and impulse as integrals

The center-of-mass frame

Variable-mass systems

Average force in a collision

Momentum conserves componentwise

Rocket equation qualitatively

Newton's second law in momentum form

The center of mass obeys Newton's second law

Motion of the center of mass

Short answer 1. Define or explain: Center of mass position

3 pts

Short answer 2. Define or explain: Ballistic pendulum sequence

3 pts

Short answer 3. Define or explain: Relative velocity reversal

3 pts

Short answer 4. Define or explain: Elastic collision special cases

3 pts

Free response

12 pts

TRANSLATION BETWEEN REPRESENTATIONS (Question 2, 12 points). A projectile of total mass 4M is launched from the ground at x = 0 and t = 0 with initial speed v0 at angle θ above the horizontal. At the highest point of its trajectory it breaks into Piece Q (mass M) and Piece R (mass 3M). At t = t1, immediately after the breakup, the two pieces move away from each other horizontally. At t = t2, Piece Q lands back at x = 0 and Piece R lands at x = x2 (Figure 1). Figure 2 (given) is a momentum bar chart immediately after launch: px = 4Mv0·cosθ and py = 4Mv0·sinθ. Figure 4 (given) shows the horizontal velocity component vx,cm of the projectile's center of mass versus t for 0 < t < t1: constant at v0·cosθ.

A. Describe the momentum bar chart at t = t1 (Figure 3): the px and py bars for Pieces Q and R, on the same scale as Figure 2 (zero components drawn as a distinct line at zero).

B. Derive an expression for x2 in terms of v0, θ, and physical constants, as appropriate.

C. Describe the lines on the Figure 4 graph representing vx versus t for Piece Q, Piece R, and the center of mass of the two-piece system for t1 < t < t2, distinctly labeled.

D. In a case where the projectile is launched identically but Piece Q falls straight down after the breakup, Piece R lands at x = xnew. Indicate whether xnew is greater than, less than, or equal to x2, and briefly justify by referencing your representations or with conceptual reasoning.