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.
Perfectly inelastic collision and maximum energy loss
Recoil
Light object striking a heavy one
Newton's second law in momentum form
Kinetic energy in the center-of-mass frame
Coefficient of restitution
Elastic collision special cases
Elastic collision in one dimension
Variable-mass systems
Perfectly elastic collision
The center-of-mass frame
Average force in a collision
Short answer 1. Define or explain: Heavy object striking a light one
3 ptsShort answer 2. Define or explain: Center of mass
3 ptsShort answer 3. Define or explain: The center of mass obeys Newton's second law
3 ptsShort answer 4. Define or explain: When momentum is conserved
3 ptsFree response
10 ptsMATHEMATICAL 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.