A block is launched up a frictionless ramp, shown below, with an initial velocit

Question

A block is launched up a frictionless ramp, shown below, with an initial velocity v0. The block travels up a ramp and continues across the level section.

1. List the forces exerted on the block after it has been launched, as it moves up the ramp. List the forces, if any, that do non-zero work. List the forces, if any, that do zero work.

Consider the same case as in the previous problem, but now we have doubled the angle so that the ramp is steeper. The ramp is still frictionless, and the block travels with the same initial velocity v0 and up to the same height H. The block travels up a ramp and continues across the level section.

2. Is the magnitude of the net work greater than, less than, or equal to the net work done in the previous problem? If it is different, how much did it change?

3. Using conservation of energy, explain how you arrived at your answer in the previous problem.

4. Now consider the case in which the ramp has an angle of 90 degrees (e.g., the ramp is entirely vertical). You can also think of this as the ball being launched directly upwards and stopping a distance H above its launch point. Is the magnitude of the net work greater than, less than, or equal to the net work done in the previous problem? Explain.

Explanation / Answer

1.)force which has non zero work = mgSin(theta)

Force whch has zero work = mg Cos9theta) or Normal

2.)remains same

work done = force * displacement

3.) 0.5mv^2 - mgh = 0.5m(v-v1)^2 = W

W = 0.5mv^2 - mgh

4.)equal to previous problem.

because we can see net displacement is same in every case i.e H.

work done = force . displacement

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