Some Energy Motion Problems

Energy/Motion problems

4. A 10-kg box is pushed by from rest by a 100-Newton force at a 30 degree angle downward with respect to the horizontal. The coefficient of friction between the box and the floor is 0.35. Determine the box's velocity (in meters/second to two decimal places) after the box has been moved through a distance of 10.99 meters.
Would increasing the angle at which the pushing force is applied increase, decrease, or not change the final velocity?

5. A 0.75 kg sphere is compressing a spring (k=15 N/m) a distance of 10 cm from its relaxed position at a 2.0 meter distance above the floor. If the sphere is released from rest it oscillates up and down as shown above. What is the sphere's velocity when it has stretched the spring a distance of 79.5 cm from its relaxed position? (to two decimal places)?

5a. At what position should the reference height be 0 for potential energy in order to maximize the calculated value for total mechanical energy?

6. A 0.05-kg block is shot from a spring-loaded gun. It travels 1.5 meters across a rough table whose coefficient of friction is .54. The force constant of the spring in the gun is 60 N/m and the table top is 0.80 meters above the floor. The spring is compressed a distance of 0.12 meters before the block is released. The block slides off the table and lands on the floor. Determine the speed of the block just before it hits the floor (to two decimal places).

6a. Name at least two variables that could be changed in this problem in order to give the block a greater speed just before impact. Please explain fully how you would change them and what effect that would have.