(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Calculate minimum value of force for a cart

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