Part I

a) Consider an object of Mass M = 7.50 kg object placed on a horizontal rough surface (μ_s = 0.400 and μ_k = 0.300) initially at rest. A force F is applied to the object, where the force is directed upward 20.0° above the horizontal. The magnitude of the force is 28.5 N. Find the speed and displacement of the object 4.55 s after the force F is applied.

b) Repeat the above problem, but the applied force F is now directed 20.0° below the horizontal. Find the speed and displacement of the object 2.00 s after the force F is applied.

Part II

An 8.00 kg mass is at rest on a frictionless incline, the angle of the incline is 32.0°. Find the speed and the change in the vertical height 3.50 seconds after the object is released.

Part III

An 8.00 kg mass is at rest on an incline, the angle of the incline is 32.0°. The incline has a rough surface (μ_s = 0.375 and μ_k = 0.250). A force F is applied to the mass, parallel to the incline, directed upward. Find the range of values the applied force F can have to keep the block motionless.

Part IV

a) An 8.00 kg mass is at rest on an incline, the angle of the incline is 32.0°. The incline has a rough surface (μ_s = 0.375 and μ_k = 0.250). A force F is applied to the mass in the horizontal direction, toward the direction up the incline. Find the force F where the motion of the object up the incline is imminent.

b) Add 2.00 N to your value for F found in part a). Calculate how fast the object is moving after a displacement of 15.0 m up the incline, and how long it would take for the object to travel this distance.