All questions should be solved using Work/or Energy.

1. A block of mass 5.2 kg slides down a frictionless ramp to a frictionless, horizontal surface. It slides along the surface for some distance and then compresses a spring to a maximum of 21 cm. The spring has a spring coefficient of 4.9 kN/m. a) Determine the height of the initial release at the top of the ramp. (3 marks) b) Determine the speed of the block when the spring is compressed 13 cm. (4 marks) c) Determine the maximum acceleration of the block while on the surface (3 marks)2. A slow-pitch machine uses a spring to fire a 198 g softball at an angle of 330 above the horizontal at a height of 1.2 m. The spring has a spring coefficient of 440 N/m and compresses 45 cm. If the average slow-pitch mound is 15.2 m away from home plate, is the slow-pitch machine properly calibrated? If the slow pitch machine is not calibrated correctly, suggest a remedy for the broken machine. (10 Marks)3. A snowboarder with a mass of 57 kg starts from a speed of 5.2 mfs at the top of a 45 m frictionless slope. The snowboarder drops down the slope and back up a second slope as per the following diagram. Determine the speed of the snowboarder at the base of the first slope, and at the top of the second slope. {5 marks} 4. A toy windup car that weighs 85 grams uses a spring with spring coefficient of 0.15 N/cm to launch itself across the floor with a friction coefficient of 0.30. If the spring compresses 0.10 m, determine the distance across the floor the car will travel. (5 Marks)5. The springs in the suspension of a car with worn-out shock absorbers will undergo SHM after hitting a bump on the road. Suppose the car with worn-out shock absorbers has two identical rear axle springs that each support 605 kg. After hitting a large pothole, the rear end of the car vibrates through six cycles in 4.4 seconds. Determine the spring coefficient of either spring. [6 Marks)