1) Hamster Pat (mass m=1 kg) is dropped from a height h=5m subject to a gravitational acceleration g = 10 m/s^2. At time t_0,
Pat lands on and compresses a massless, frictionless spring (k= 4 N/m) and
Pat is brought to rest at time t_1. a) What is the maximum spring compression
in meters? b) What is the power delivered to the spring at time t_0 and
at time t_1? c) Find the power P(x) as a function of compression distance
x and the maximum power.
2) A 90 degree cone of base radius r and mass M rests on a frictionless table. Pat (mass m) is nudged off the tip and slides without friction down the
cone. What is the speed of the cone when Pat hits the table? What is the
displacement of the cone at this time?
3) Two billiard balls of mass m and radius r collide and stick together. Suppose one (the eight ball)
is at rest at the origin in the lab, while the center of the other (the cue ball) has speed v along the
x axis and position x=0, y=2r at the time of impact. a) What is the angular
velocity of the system in the cm frame after the collision? b) What is the
change in kinetic energy of the system in this frame?
4) Having messed up the demonstration,
instructor Pat (mass m, height h) falls over "like a tree". What is the
gravitational torque about Pat's feet when Pat is tipped by 45 degrees?
With what speed does Pat's head hit the ground?