Force and Translational Dynamics 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 59 terms and is the same for everyone, so a teacher can assign “Unit 2, Paper 2” 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

Angle of repose

How friction widens the safe speeds on a bank

Solving the terminal velocity differential equation

Coefficients of friction are dimensionless

Non-inertial frames

Minimum force to prevent slipping

Gravity inside a uniform sphere

Terminal velocity from a drag law

Circular motion dynamics

Atwood machine

Pulley constraints

Orbits and Kepler's third law

Short answer 1. Define or explain: Newton's law of gravitation

3 pts

Short answer 2. Define or explain: Tension in an ideal string

3 pts

Short answer 3. Define or explain: Velocity-dependent drag

3 pts

Short answer 4. Define or explain: Approach to terminal velocity

3 pts

Free response

10 pts

MATHEMATICAL ROUTINES (Question 1, 10 points). A box of mass M slides to the right on a frictionless horizontal surface. A small cube, also of mass M, is inside the box, pressed against the box's right wall and held above the box's floor (Figure 1). The coefficients of static and kinetic friction between cube and wall are μs and μk, with μs > μk. A resistive force F_R = −bv (b a positive constant) acts on the box, so the box slows. At t = 0 the box-cube system slides right with speed v0. For 0 ≤ t < tcrit, the cube stays against the wall at constant height; at t = tcrit the cube begins to slide down the wall.

A(i). The normal force from the wall on the cube has magnitude FN. Determine an expression for the magnitude of the cube’s acceleration in terms of M, FN, and physical constants.

A(ii). Derive an expression for FN as a function of t from t = 0 until just before the cube reaches the bottom of the box, in terms of M, b, v0, t, and physical constants.

A(iii). Describe the graph of the magnitude Ff of the frictional force on the cube from the wall as a function of t over the same interval.

B. Derive an expression for tcrit in terms of M, b, μs, v0, and physical constants.