Question

• Cooper is standing on a 45◦ hill. He kicks a rock (m = 1kg) with a force of F = 50N down the hill. His foot is in contact with the rock for 0.1 seconds. How fast will the rock be moving after 5 seconds? How long does it take for the rock to travel 100 meters? Ignore pesky friction and rotation.

• When an object is falling, it is said to be at terminal velocity if it is no longer accelerating as it falls. The air resistance (drag) on Fiona as she jumps from a plane is given by the equation Fd = kAv2 , where v is her velocity, A is her crosssectional area, and k is a constant with proper units. She then opens a parachute, increasing her cross-sectional area by a factor of 100. What is the ratio of her terminal velocity with the parachute to that without the parachute?

• When runners turn a corner, they often tilt their entire body off of vertical into the turn. Why do they do this?

• A rock of mass m is tied to the end of a massless spring of length l and spring constant k. The rock is then spun in a circle at constant velocity v. How far does the spring stretch as a result of this motion?

• Artificial gravity occurs due to the normal force when you stand inside a cylinder which rotates about its axis. One proposition for long-term space travel is to include such a rotating cylinder on spacecraft. Supposing we want the artificial gravity to match the real gravity of Earth and the cylinder has a radius of 30m, how fast must the cylinder rotate?

Answer 1

The solution for first question is given below

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