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.
Gravitational field inside a sphere
Vertical circular motion condition
Terminal velocity from a drag law
Pulley constraints
Banked curve with friction
Systems with multiple bodies
Solving a separable equation of motion
Gravitational potential energy sign
Total energy of a circular orbit
Inclined plane analysis
Free-body diagram discipline
Solving the terminal velocity differential equation
Short answer 1. Define or explain: Newton's law of gravitation
3 ptsShort answer 2. Define or explain: Newton's second law in general form
3 ptsShort answer 3. Define or explain: Impulse from a variable force
3 ptsShort answer 4. Define or explain: Orbits and Kepler's third law
3 ptsFree response
10 ptsA 0.20 kg sphere is released from rest and falls through air that exerts a drag force of magnitude bv opposite to the velocity, with b = 0.40 kg/s. Take g = 9.8 m/s² and take downward as positive.
Describe the free-body diagram and write Newton’s second law as a differential equation for v(t).
Determine the terminal speed.
Show that v(t) = v_t(1 − e^(−bt/m)) satisfies your differential equation and the initial condition, and identify the time constant.
Calculate the time at which the sphere reaches half its terminal speed.
Describe the shape of the v-versus-t and a-versus-t graphs, labeling asymptotes and intercepts, and state the acceleration at t = 0.