- #1

- 4

- 0

## Homework Statement

A small block of mass

*m*starts from rest and slides along a frictionless loop-the-loop as shown in the image. What should be the initial height

*h*, so that

*m*pushes against the top of the track (at

*a*) with a force equal to its weight?

Ans.

*h*=3R

## Homework Equations

KE=(1/2)mv

^{2}

PE=mgh

F

_{c}=mv

^{2}/r

## The Attempt at a Solution

PE

_{i}=mgh

KE

_{a}=PE

_{i}-PE

_{a}=mgh-2mgR

(1/2)m(v

_{a})

^{2}=mgh-2mgR

v

_{a}=√(2gh-4gR)

F

_{c}=mg

mg=(2mgh-4mgR)/R

2h-4R=R

h=(5/2)R

I think I attempted the problem in the correct manner, but perhaps made a subtle algebraic mistake since the coefficient is only off by 1/2.