Loop-the-Loop, work-energy problem

[armolinasf]

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

radial acceleration=5gR/R=5g=49m/s^2

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

Thanks for the help

 

[PhanthomJay]

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.

radial acceleration=5gR/R=5g=49m/s^2

correct your error in calculating v

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

To find the tangential acceleration at the top of the loop, you should first find the tangential net force at the top of the loop, then use Newton's laws. What is the tangential (horizontal) net force at the top of the loop?