2. Pushing a rock: A worker is pushing a spherical rock of radius 0.5 meters and mass 1000 kilograms. She accidentally pushes the rock over the edge of a hill and loses control of it. At the moment she lets go of it the boulder is 1.0 meters from the bottom of the hill, which is at an angle of 5 degrees above the horizontal. When she lets go the center of mass of the boulder is moving at 1.0 m/s. How fast is it moving at the bottom of the hill? 1.0m 5°

1.A 1500-N force is required to raise an aluminum slab (the density of aluminum is 2700 kg/m3 ) to a surface of an ocean. The force required to lift it out of the water is approximately 2.A 6-kg stone moving north at 3 m/s collides with a 4-kg lump of clay moving west at 2 m/s. The stone becomes embedded in the clay. What is the speed of the composite body after the collision? 3.A barge is 5 m wide and 7 m long. When a bulldozer pulls onto the barge, it sinks 3 cm lower in the sea water. What is the weight of the bulldozer? 4.The object shown rotates about an axis perpendicular to the paper and through point P. The kinetic energy of the object is equal to 5.6 J. If M = 1.5 kg and L = 0.75 m, what is the angular velocity of the object? Neglect the mass of the connecting rods and treat the masses as particles. 5.What would a person who weighs 700 N on the earth weigh on a planet whose mass and radius were both 1/3 those of the earth? 6.A 3-kg particle moves in the xy plane with a…

6. Two smooth disks A and B (masses 0.8 and 0.6 kg, respectively) move with velocities as pictured and collide in such a way that the coefficient of restitution is 0.75. Determine the velocities of each disk just after the collision. B (VB)1 = 4 m/s (VA)1 = 6 m/s A -X

The linear mass density of a straight rod of length L is given by a = a +?x (kg/m). Here x is the distance measured from A. The center of mass of the rod is xem = (-)L (m) away from the A end of the rod. What is the relationship between a and b? A x = 0 x = L A) a = 2b B) a = b C) a = b D) a = b E) a =b

1. A carnival ride consists of a hollow cylinder spinning about a vertical axis. As the cylinder spins with a speed vo, a person of mass M rides the inside wall of the cylinder without slipping down (there is no floor). The distance of the center of mass of the person from the axis of the cylinder is R. a. Draw the free body diagram of forces acting on the person during the ride. Show your choice for the +x and +y directions. b. Write out Newton's 2nd law in the x and y directions. Set the RHS of the equations to zero or Mv²/R or –Mv²/R. X: y: c. What is the normal force? d. What is the magnitude and direction of the friction force that the wall exerts on the rider? e. What is the magnitude and direction of the friction force the rider exerts on the wall? f. The coefficient of static friction between the wall and the rider is µg. What is the minimum speed that the rider can move without slipping down the wall?

PROBLEM 4: Solid spheres A and B with both of each mass of 2 kgs undergo a direct central impact. Before impact, A is moving to the right with a velocity of 4 m/s and B is stationary. Determine the velocity of A after impact if the impact is perfectly plastic.

Follow-up Questions 2. Three uniform thin rods, each of length L, form an inverted U. The ogo vertical rods each have a mass of M: the horizontal rod has a mass of 3M. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass? L. Part 48

4. Object A, whose center is at (2.0m, 2.0m) has a mass of 40 kg. Object B has its center at (10m, 4.0m) and has a mass of 30 kg. What is the x component of their center of mass in m? a) 2.9 6. b) 5.4 B c) 6.1 4. d) 6.3 A e) 6.7 2 8. 10 12 x (m) 6. 2) (w)m)

Kramer goes bowling and decides to employ the force of gravity to "pick up a spare." He rolls the 6.50 kg bowling ball very slowly so that it comes to rest a center-to-center distance of 0.245 m from the one remaining 2.00 kg bowling pin. Treat both the ball and the pin as point objects, and determine the magnitude of the force of gravity ?⃗ grav between them.

4. A fisherman in a boat catches a shark with a harpoon. The shark struggles for a while and then becomes limp when at a distance of 300 m from the boat. The fisherman pulls the shark all the way to the boat by the rope attached to the harpoon. During this operation, the boat (initially at rest) moves 45 m in the direction of the shark. The mass of the boat is 5400 kg. What is the mass of the shark? Pretend that the water exerts no friction. (Hint: Friction is ignored, so there are no external forces, and the center of mass of the system (the shark and boat) should not move at all.) A) 953 kg B) 477 kg C) 318 kg from the left and of