a) Calculate the height that m 2 moves up the bowl after the collision (measured vertically from the bottom of the bowl).

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2 2. A small mass m 1 slides in a completely frictionless spherical bowl. m 1 starts at rest at height h = ½ R above the bottom of the bowl. When it reaches the bottom of the bowl it strikes a mass m 2, where m 2 = 3m 1, in a completely elastic collision. a) Calculate the height that m 2 moves up the bowl after the collision (measured vertically from the bottom of the bowl). b) Calculate the height that m 1 moves up the bowl after the collision.

3 3. A kg skeet is fired at an angle of 30 0 to the horizontal with a speed of 30 m/s. When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200 m/s. The pellet is embedded in the skeet. a) How much higher does the skeet go up? b) How much extra distance x, does the skeet travel because of the collision?

4 4. A proton with a speed of 8.2 X 10 5 m/s collides elastically with a stationary proton in a hydrogen atom. One proton of the protons is observed to be scattered at a 60 0 angle. Calculate the trajectory of the other proton, and the velocities of the protons after the collision. 5. A person of mass M = 32.5 kg on ice disdainfully throws my PY 205 text book with mass m = 2.25 kg at v b = 12 m/s. The book is thrown from height of 2 m and the total distance between the book and the offender is 15.2 m when the book lands. a) At what angle was this awesome book thrown? b) How fast is the offender moving?

5 6. A 70-kg stuntman takes off straight upwards from the ground wearing a jet pack that burns 2.0 kg of fuel per second and ejects the burned fuel vertically downward at an exhaust speed of 750 m/s (relative to the pack). The initial mass of fuel is 50 kg, while the non-fuel parts of the jet pack have a mass of 20 kg. Find the stuntman's velocity at the moment the fuel runs out. Neglect air resistance and any change of the gravitational constant g with altitude. 7. (Choose two) a) A plate of uniform thickness t and uniform density ρ has the shape of a square of sides L containing two holes: one a circle of radius r centered on the middle of the square outer perimeter; the other a small square of sides d, centered three-quarters of the way along the diagonal leading from the plate's bottom left corner to its top right corner. Calculate the distance of the plate's center of mass from its bottom left corner. b) A bullet of mass 60 g is fired from a gun with an initial velocity of 150 m/s at an angle of 50 0 above the horizontal ground. During its flight, the bullet explodes into two fragments: one of mass 10 g, the other of mass 50 g. The internal forces acting on the fragments during the explosion are directed horizontally and within the vertical plane that contains the bullet's trajectory before the explosion. The lighter fragment

6 eventually hits the ground 3.7 km from the gun. How far from the gun does the heavier fragment land? Neglect air resistance. c) Find the center of mass of a rod whose density varies with distance from one end as λ = λ 0 x 2 8. A mass m 1 suspended on a string of length L is released from rest with, the string horizontal, as shown in the diagram. At the lowest point in its swing, m 1 collides elastically with a stationary mass m 2 = 2m 1 suspended on a string of length L. Calculate the maximum angle that the string suspending m 2 makes with the vertical following the initial collision. 9. A block of mass M = 1.0 kg contains a coiled spring and a ball of mass m = 0.25 kg. The spring is released when the block-ball system is at rest at the edge of a frictionless plane inclined 20 0 from the horizontal (see diagram). The ball, initially 2.0 m above a horizontal floor, strikes the floor a horizontal distance of 3.0 m from the release point.

7 a) How far along the plane does the block move before coming to rest? b) How much energy was initially stored in the spring? 10. A rocket sled is used to test the reaction of humans to large accelerations. The sled slides on a low friction track with coefficient of µ K = 0.2. The sled, passenger, and fuel have a combined initial mass of 1000 kg and the fuel emerges from the rocket with a relative speed of 300 m/s. The rocket sled starts from rest and bums all its fuel at a uniform rate in 4 seconds. When the fuel has been exhausted, the remaining sled and passenger have a mass of 300 kg. a) Find the maximum speed attained by the sled, b) Find the maximum acceleration experienced by the passenger, expressed in g s. 11. Two cars approach an intersection as shown. Car 1 weighs 4500 lbs and has a speed of 55.0 mi/hr. Car 2 weighs 3750 pounds with a speed of 60.0 mi/hr. They collide in a completely inelastic collision at the intersection.

8 a) Calculate the direction the wreckage moves after the collision. Express this as an angle measured counterclockwise from the positive x-axis. b) If the coefficient of kinetic friction is 0.55 for the tires on this road, and the wheels of the car are locked (not rolling), calculate the distance the wreckage slides from the collision point.