Question

Please answer all of them, Thank you.

1. What are the three equivalent definitions of a conservative force? Show how they are equivalent.

2. Suppose there is a pendulum with length 5m hanging from a ceiling. A ball of mass 2kg is attached to the bottom of the pendulum. The ball begins at rest. If I give the ball a velocity of
6 m/s, what is the maximum height that the ball will achieve? Use the energy conservation model to solve, and assume that there is no friction or air resistance.

3. I hang a (massless) spring from the ceiling. When the spring is lying horizontally, it has equilibrium length of 0.75m, but a longer equilibrium length once it is hanging from the ceiling with a mass attached (see previous homework). I then attach a block with mass 0.5kg to the bottom of the spring and let the system come to equilibrium. If the block starts at rest, how much speed must I give it so that strikes the ceiling? How far will it stretch the spring when it bounces back?

4. For the following situations given the system described, which of the quantities listed should be zero? For those that are not zero, provide its sign. (External work, change in kinetic energy, change in gravitational potential energy, change in elastic potential energy, change in thermal energy)

a. System: Ice skater. Situation: (Initial state = Ice skater at rest on ice, final state: ice skater at high speed on the ice)

b. System: Ice skater + ice rink. Situation: (Initial state = Ice skater at rest on ice, final state: ice skater at high speed on the ice)

c. System: Earth + comet. Situation: (Initial state = comet is far from earth, final state = comet has fallen to Earth, right before it impacts the ground)

d. System: Earth + hanging spring with mass attached. Situation: (Initial state = mass at rest at equilibrium position, final state = mass at rest with spring fully compressed)

Answer 1