Question

You land in a spring-loaded cart (k=144 kN/m) (m=500kg) which instantly launches you along a 3.5m track (Mu-(0.1,0.05) that then enters a loop that has a height of 10m at the top.

a. If your speed at the top of the loop is 12 m/s what is the initial compression of the spring? (constant friction)

b. If the loop continues around and then launches off a 3.5m long, 30 degrees incline, how high will it fly?

I use these to check my work so please make it legible.  

Answer 1

a) At the top of the loop.

Potential Energy = mgh = 500*9.81*10 = 49050 J

Kinetic Energy = 0.5mv² = 0.5*500*12² = 36000J

Energy Lost due to friction =

Thus this energy needs to be provided by the spring. Thus if it compresses by x then

Answer: 1.092 m

b) The energy lost due to friction over a 3.5 m long 30 degree incline is

Potential energy when it reaches it's highest point = 49050+36000-743.375 = 84306.625J

The height it will reach is given by

Answer: 17.188 m