Part A) A 10-kg cart is initially at rest at the top of a frictionless track of
ID: 1357572 • Letter: P
Question
Part A) A 10-kg cart is initially at rest at the top of a frictionless track of height H = 16 m. It travels down the track and around the inside of a loop whose radius is R = 5 m. What is the contact force (in N) exerted by the track on the cart when the cart is at the top of the loop (at point B)? Hint: first conserve energy.
(a) 212.8 (b) 137.2 (c) 176.2 (d) 115.9 (e) None of these
Part B) In the previous problem, imagine now that the track is not frictionless, and that the speed of the cart at the top of the loop is 7.0 m/s, and further suppose that the distance that the cart travels along the track from the top of the hill to the top of the loop is 36 meters. What must have been the magnitude of the frictional force (in N) acting on the cart?
(a) 4.5 (b) 3.4 (c) 9.5 (d) 7.5 (e) None of these
The answers are B and C, but I don't know why.
Explanation / Answer
A) Using energy conservation, ( PE + KE)
10 x 9.81 x 16 + 0 = 10 x 9.81 x 10 + 10 v^2 /2
v = 10.85 m/s
now at top.
N + mg = mv^2 /r
N = 10 ( 10.85^2 /5 - 9.81) = 137.35 N
Ans (b)
B) work done by gravity + work done by fricton = change in KE
10 x 9.81 x 6 - ( 36 x f) = 10 x 7^2 /2 - 0
f = 9.5 N
Ans (c)