# Loop-the-Loop, work-energy problem

## Homework Statement

A car starts at a point A at a height H above the bottom of the loop the loop. It is starting from rest and we ignore friction.

A) what is minimum value of H in terms of R such that the car moves around the loop without falling off at the top point B.

B) If R=20m and H=3.5R calculate the speed, radial and tangential acceleration

## The Attempt at a Solution

A) total energy at A is equal to mgH. total energy at B is equal to mg2R + .5mv^2

Solving for H gives H=2R+v^2/2g. Minimum velocity at B is mg=(mv^2/R) V62=Rg

Substituting gives H=5/2R. Not sure if this is correct....

B) to find speed: mg(3.5R)=mgR+.5mv^2, masses cancel. v=sqrt(5gR)=sqrt(5*9.8*20)=31.3m/s

I don't know how to find tangential acceleration....

Thanks for the help

## Answers and Replies

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PhanthomJay
Homework Helper
Gold Member

## Homework Statement

A car starts at a point A at a height H above the bottom of the loop the loop. It is starting from rest and we ignore friction.

A) what is minimum value of H in terms of R such that the car moves around the loop without falling off at the top point B.

B) If R=20m and H=3.5R calculate the speed, radial and tangential acceleration

## The Attempt at a Solution

A) total energy at A is equal to mgH. total energy at B is equal to mg2R + .5mv^2

Solving for H gives H=2R+v^2/2g. Minimum velocity at B is mg=(mv^2/R) V62=Rg

Substituting gives H=5/2R. Not sure if this is correct....
yes, but be sure to right it correctly .... H = (5/2)R = 2.5 R
B) to find speed: mg(3.5R)=mgR .....
whoops, that's 2mgR + ...etc.