Work, Energy, and Power 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.
Deriving force from U(x)
Gravitational potential energy in general
Potential energy curves
Stability from a potential curve
Escape energy
Work done by a variable force from a graph
Spring potential energy
Turning points
Work done by friction
Conservative forces and path independence
Reading kinetic energy from a potential curve
When to use energy rather than forces
Short answer 1. Define or explain: Power delivered by a constant force
3 ptsShort answer 2. Define or explain: Energy in a spring-mass system
3 ptsShort answer 3. Define or explain: Work-energy theorem
3 ptsShort answer 4. Define or explain: Instantaneous power
3 ptsFree response
10 ptsA 0.50 kg particle moves along the x-axis in a region where its potential energy is U(x) = 2x³ − 9x² + 12x, with U in joules and x in meters. (a) Determine the force F(x) on the particle. (b) Find all positions of equilibrium and classify each as stable or unstable, justifying with a second derivative. (c) The particle is released from rest at x = 2.5 m. Determine its total mechanical energy and its speed as it passes x = 2.0 m. (d) Determine whether the particle released in part (c) can reach x = 0.50 m, and describe the resulting motion. (e) A second particle of the same mass is displaced slightly from x = 2.0 m. Determine the period of its small oscillations.