Some Questions concerning Work, Energy and motion...

1. A cyclist starts from rest and freewheels down a hill inclined at **arcsin 1/20** to the horizontal. After traveling **80 m** the road becomes horizontal and the cyclist travels another **80 m** before coming to rest without using his brakes. Given that the combined mass of the cyclist and his machine is **80 kg**, model the cyclist and his machine as a single particle and hence find the **resistive force**, assumed constant throughout the motion.

2. A boy and his skateboard have a mass of **50 kg**. He descends a slope inclined at **12(degrees)** to the horizontal from rest. At the bottom, the ground becomes horizontal for **10 m** before rising at **8(degrees)** to the horizontal. The boy travels **30 m** up the incline before coming to rest again. He is subject to a constant resistance of **20 N** throughout the motion. By modeling the boy and his skateboard as a single particle find the **distance** the boy traveled down the slope.

3. A book slides down a rough desk lid which is inclined at **30(degrees)** to the horizontal and falls to the ground which is **0.8 m** below the edge of the lid. The **coefficient of friction** between the book and the lid is **1/4**. Given that the book starts from rest **0.4 m** from the bottom of the lid which is hinged is at the edge of the desk, find the **speed** with which the book hits the floor.

4. A rough plane is inclined at **arcsin 3/5** to the horizontal. A package of mass **40 kg** is released from rest and travels **15 m** while increasing speed to **12 m/s**. Find, using energy considerations, the **coefficient of friction** between the package and the plane.

Im revising for my Mechanics 2 A2 Level exam so ill be really grateful.... Thankyou....(Bow)