Homework Help: Calculate minimum value of force for a cart

1. Dec 3, 2008

Inertialforce

1. The problem statement, all variables and given/known data
Given the diagram shown, calculate the minimum value of h such that when the cart reaches point A, it is just about to fall off.

R = 10m
mass of cart = 158kg
note: there is no friction in the entire system

2. Relevant equations
ΣFc = mac
(note: Fc = centripetal force and ac = centripetal acceleration)

3. The attempt at a solution
I am not sure if I got this question right but here is what I did:

First I drew a free body diagram for the part of the diagram that had centripetal forces acting on it (included in the attachments).

Then for my calculations I started out with the equation ΣFc = mac first and here is what I did:

ΣFc = mac
Fn + Fg = mv^2/r (Fn cancels out therefore):
Fg = mv^2/r
mg = mv^2/r (the m's cancel out)
g = v^2/r
(g)(r) = v^2
(9.80)(10) = v^2
98 = v^2

there is no friction in the system therefore:
ΔE = 0
(Epf - Epi) + (Ekf - Eki) = 0
Epf - Epi + Ekf - Eki = 0
Epf + Ekf = Epi + Eki (Eki = 0 therefore):
Epf + Ekf = Epi
mghf + 1/2mvf^2 = mghi (the m's cancel out):
ghf + 1/2vf^2 = ghi
(9.80)(2*10) + 1/2(98) = (9.80)hi (for here I put hf = 2R because the cart is at the very top of the loop here so therefore hf = 2 times the radius)
245/9.80 = hi
25m = hi

My question is, could someone please check this question to see if I did it right or if my answer is right, because I have three questions following this one that are quite similar in setup so I just want to make sure I am doing the first one correctly before I move onto the other three.

Attached Files:

File size:
24.5 KB
Views:
53
• Gravitation Free Body Diagram.doc
File size:
23.5 KB
Views:
58
Last edited: Dec 3, 2008
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted