A ball is dropped from a height on a frictionless loop-de-loop of radius = [R] m. What is the smallest that can be where the ball makes it around the track without losing contact? Please give your answer in units of m.

In the arrangement shown here, = [m1] kg, = [m2] kg, and the pulley and rope are essentially massless and frictionless. We release the system from rest when is a distance = [h] cm above the table. (Q27 answer 2 pts, Q28 work 5 pts) What is the speed of at the instant it hits the table? When hits the table, the rope breaks. (Q29, 7 pts) To what maximum height above the table does rise to through the course of its motion? (Q30, 7 pts) At what speed does then hit the table? To continue, please enter the speed of hitting the table (part a).

Forces acting on an object will cause an acceleration.

If a flea can jump straight up to a height of = [h] cm, how long is it in the air? Please give your answer in units of ms.

Shown here is a plot of velocity as a function of time. What is the average acceleration over the first 5 seconds?

A block of ice with mass = [m] kg is released from rest at the top of a ramp of length

A mass = [m] kg is tied to a rope that is wrapped around a pulley and connected to a spring with spring constant = [k] N/m. The rope and pulley are essentially massless and frictionless. At the initial position of the system (illustrated by top block), the spring is at equilibrium length. When the block has dropped a distance , the system is again at rest. What is the value of ? Please give your answer in units of m.

If you were stacking credit cards (just laying them flat, no crazy house of cards), how many cards would be needed to stack from floor to ceiling in a typical room?

A mass = [m] kg is tied to a rope that is wrapped around a pulley and connected to a spring with spring constant . The rope and pulley are essentially massless and frictionless. At the initial position of the system (illustrated by top block), the spring is at equilibrium length. When the block has dropped a distance = [d] m, the system is again at rest. What is the value of the spring constant ? Please give your answer in units of N/m.

In this system, the rope and pulley have negligible mass and the pulley is frictionless but there is friction between and the ramp. The ramp has an incline angle