The model of a roller coaster consists of a ramp and circular loops. A small block of mass M starts from height H with speed V=0 and slides without friction down the ramp and around the inside of the loop of radius H/2. Position P is a point on the loop at an angle of θ with the horizontal. express all algebraic answers in terms of M, H,θ, and fundamental constants.

1. Derive an expression for the speed of the block at position P.

2. Derive an expression for the magnitude of the force exerted by the loop on the block when it is at position P

3. Calculate the angle θL in degrees at which the block leaves the loop

4. The block is replaced with a sphere that also starts at heigh H. Now there is enough friction to allow the sphere to roll down the ramp without slipping, Identify how the new angle θn at which the sphere leaves the loop compares with the angle θl calculated in part 3. Then explain your reasoning