3 A child of mass 20 kg on a swing hanging from a 3.0m chain is pulled by her uncle until the swing is at an angle of 30 degrees to the vertical. a) How much farther from the ground is the child now, compared to when the swing was hanging straight down? b) Since the child is motionless at he beginning and the end of the process, what can you say about the work done by gravity, and the work done by the puller on the child during the pullback? What is the amount of work her uncle does to pull back the swing? c) If he lets the swing go at this point, what is the child's speed as she passes the lowest point of the swing & the chain is vertical? Ignore the mass of the swing seat & chain.

A factory worker moves a 23.0 kgkg crate a distance of 4.50 mm along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is 0.300.   What magnitude of force must the worker apply?   How much work is done on the crate by the worker's push?   How much work is done on the crate by friction?   How much work is done by the normal force and by the gravity?   What is the net work done on the crate?

Consider a rope lowering a mass m=2.45kg at a constant speed v=8.73 m/s down a distance of d=5.72 m as shown in the figure below.  c) What is the work done on the mass by the tension in the rope as it descends a distance d=5.72 m? d) What is the change in kinetic energy of the mass as it descends a distance d=5.72 m?

QUESTION 16 A crate of mass, m, slides down a plane inclined at an angle, 0, to the horizontal for a distance x down the incline. If the coefficient of kinetic friction between the inclined surface and the crate is µk. what is the work done by friction? a. -Hkmgxcose b. -mgxcose C. -mgxcose/µk d. -µkmgxtane e. -mgxsin0

4. This Olympic skeleton athlete slides down an icy track head first. The track has many twists and turns with a total height of 102.75 m. If the 99.375 kg man has a speed of 27 m/s at the bottom, what was the total work done on him by friction and air resistance slowing him down? (In other words, what was the energy lost to friction and air resistance?) He starts from rest at the top. Previous submissions:

1. A 23.0 kg child is playing on a swing with a length of 2.5 m. If the swing starts from rest and makes an angle of 40.0◦ with the vertical at the top of the swing, a) determine the child’s speed at the bottom of the swing neglecting friction. b) If the swing has a speed of 2.8 m/s at the bottom, determine the work done by friction during the downswing and, bonus) assuming the force of friction is constant, determine the maximum angle the swing attains on the upswing after passing through the bottom. Hint: Use the approximation that cos θ ≈ 1 − 1 2 θ 2 for angles given in radians.