Assignment:
Problems:
1) The potential energy function of a certain force acting on an object is U(x) = 3x3 - 5x + 9. Calculate the force on the object when the object is at x = 2 m.
2) A uniform sheet of wood 6 m on a side has a square piece 2 m on a side cut out of it. The cut-out is centered vertically on the right side of the sheet. The center of the sheet is located at the origin. See diagram. Find the center of mass of the sheet.
3) A cubical box has been constructed from metal plates of uniform density and negligible thickness. The box is open at the top. See diagram. The sides of the cube are 40 cm. Find the x, y, and z coordinates of the center of mass of the box.
4) Three cricket balls have masses of 4 kg, 6 kg, and 8 kg, respectively. The ball A has a velocity of 12 m/s while the other balls are initially at rest. The ball A collides with the ball B and rebounds in the opposite direction with a velocity of 7 m/s. (a) Calculate the momentum of ball A before the first collision. (b) Calculate the velocity of ball B after the first collision. Ball B now hits ball C (which has gum on it) and sticks to it. (c) What is the velocity of the balls after this second collision?
5) A 3 kg sphere moving at 30 m/s makes a perfectly inelastic collision with a second sphere that is at rest. The spheres have a velocity of 10 m/s after the collision. (a) What is the mass of the second sphere? (b) How much kinetic energy is lost in the collision?
6) Skid of weight 440 N is stuck in the middle of a circular frozen pond of radius 5 m. He cannot move because the pond is absolutely frictionless. He happens to have his 2.6 kg physics textbook so he looks for a solution to his problem. Unable to find a solution he throws his physics textbook in a fit a rage. Skid throws it at a velocity of 4 m/s directly away from him. After throwing the book, how long does it take Skid to reach the edge of the pond?
7) A 4 g object moving to the right at 20 cm/s makes an elastic head-on collision with a 10 g object moving to the left at 5 cm/s. Calculate the velocity of each ball after the collision.
8) Skid is driving in his car of 2400 kg at 80 m/s towards Mitch. Mitch is driving in his car of 1600 kg at 60 m/s towards Skid. Calculate the velocity of the center of mass of the Skid/Mitch system.
9) Greezy-X of 50 kg is standing at the end of a flatboat of 180 kg and is 6 m from the shore. See diagram. Greezy then walks to the other end of the 4 m long boat. Assume there is no friction between the boat and the water. Calculate how far Greezy is from shore. HINT: Think about what the center of mass is doing before, during, and after he walks the across the boat.
10) In a game of pool, the cue ball with 5 m/s makes an elastic collision with the 8 ball which is initially at rest. After the collision, the 8 ball moves off at an angle of 30° with respect to the original direction of the cue ball. Assume that each ball has the same mass. (a) Find the direction of motion of the cue ball after the impact. (b) Calculate the speed of each ball after the collision.
11) A steel ball of mass 3 kg strikes a solid wall at 10 m/s at an angle of 60°. It bounces off the wall with the same speed and angle. See diagram. If the ball is in contact with the wall for 0.2 s, what is the average force exerted on the ball by the wall? Hint: Think velocity components.
