# Week 10

Reading: PSE Chap 7, Work and Energy
Topics: This week, we begin discussing the concepts of work, kinetic and potential energy, energy conservation, and power

Lab:

Homework Problems: Due on Wed. Oct. 26.

1. Sled on a pond: Solution. A sled of mass m is given a kick so it is sliding across a frozen pond at an initial speed of 2 m/s. The coefficient of kinetic friction between the sled and the ice is 0.10. Using energy considerations, find the distance the sled moves before coming to a stop. Hint: the friction force is doing work on the sled.
2. Climbing gymnast: Solution. A 50 kg gymnast climbs a 10 meter high vertical rope in 5 seconds. Find the average power output of the gymnast in climbing the rope.
3. Work on a particle. Solution. A 4.0 kg particle is moving along the x-axis. Its position varies according to x(t) = t + 2.0 * t^3. x(t) is in meters and t is in seconds.
• Find the kinetic energy at any time, t. Hint: use calculus.
• Find the acceleration and the force acting on it at time t.
• Find the power delivered to the particle at time t.
• Find the work done on the particle in the time interval between 0 and 2 seconds.
4. Spring gun: Solution. A spring gun is used to launch a stainless steel ball straight up into the air. The spring constant is 10 Newton per centimeter. The spring is compressed 2 cm. Assume the ball weights 100 grams and that the spring itself is massless and frictionless. What is the muzzle velocity of the ball at the moment it leaves the gun? Hint: the change is kinetic energy is equal to the -net- work done on the ball. There are two forces doing work on the ball. Now: how would your answer change if the gun is aimed at a 45 degree angle? Is the muzzle velocity the same?

Quiz: We will have a quiz on Monday, Oct. 17 covering Newton's laws of motion, including friction, drag, and centripetal force.