• Support PF! Buy your school textbooks, materials and every day products Here!

Circular Motion Loop question

  • #1

Homework Statement



Bob starts at rest from the top of a frictionless ramp. At the bottom of the ramp, he enters a frictionless circular loop. The total mass of the child and the cart he sits in his m. What must the height of the ramp be in order for the cart to successfully traverse the loop.

r = radius of loop
h = height of ramp
theta = angle of the ramp (irrelevant though)

Homework Equations




The Attempt at a Solution


[/B]
I solved for the minimum speed at the top of the loop.

Fy = F + mg = mv^2/r

v= sqrt(rg)

I then used conservation of energy.

Initial : mgh
Final : mg2r + (m(sqrt(rg))^2)/2

mgh = mg2r + mrg/2

mgh = 5mgr/2

Cancel stuff out h = 5r/2 (WRONG)

Instead the solution calls for using kinematics not energy conservation.

v= sqrt(rg) stills hold.

vf^2 = vi^2 + 2ax

rg = 0 + 2gsin(theta)*(h/sin(theta)

rg = 2gh

r = 2h

h = r/2 (CORRECT answer)

I understand the mathematical process of the correct solution.
However, I don't understand why I can't use conservation of energy(gives me wrong answer) instead of kinematics.







 

Attachments

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
32,730
5,030
The second answer (r/2) is clearly wrong since it would not provide enough energy to reach the top of the loop even with no remaining KE.
The calculation goes wrong because it equates the speed at the bottom of the ramp to that required at the top of the loop.
The first answer is correct.
 
  • #3
The solutions I have showed the second answer as the correct answer.
The second answer (r/2) is clearly wrong since it would not provide enough energy to reach the top of the loop even with no remaining KE.
The calculation goes wrong because it equates the speed at the bottom of the ramp to that required at the top of the loop.
The first answer is correct.
Really? That's the solution provided to me.
Glad to know I wasn't paranoid or something.

Is there any additional information that would make solving this question using kinematic possible, then?
 
  • #4
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
32,730
5,030
Is there any additional information that would make solving this question using kinematic possible, then?
The v2-u2=2as equation is effectively KE+PE constant. All that's different is factoring out the mass.
 

Related Threads on Circular Motion Loop question

  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
3
Views
624
Replies
3
Views
3K
  • Last Post
Replies
19
Views
917
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
4
Views
1K
Replies
3
Views
2K
  • Last Post
Replies
1
Views
3K
Replies
7
Views
470
Replies
1
Views
3K
Top