The small mass m sliding without friction along the looped track shown in the fi
ID: 1443130 • Letter: T
Question
The small mass m sliding without friction along the looped track shown in the figure(Figure 1) is to remain on the track at all times, even at the very top of the loop of radius r.
a) If the actual release height is 3 h, calculate the normal force exerted by the track at the bottom of the loop.
b) If the actual release height is 5 h, calculate the normal force exerted by the track at the top of the loop.
c) If the actual release height is 9 h, calculate the normal force exerted by the track after the block exits the loop onto the flat section.
Explanation / Answer
a) Using energy conservation to find speed at bottom of loop:
PE + KE = constant
mg(3h) + 0 = m v^2 /2 + 0
v = sqrt(6gh)
at bottom position,
using Fnet = ma
N - mg = mv^2 /r
N = mg + m (6gh)/r = mg (6h/r + 1 )
b)
PE + KE = constant
mg(5h) + 0 = m v^2 /2 + mg(2r)
v = sqrt(10gh - 4gr)
at bottom position,
using Fnet = ma
N + mg = mv^2 /r
N = m (10gh - 4gr)/r - mg = mg (10h/r - 4 - 1 )
N = mg(10h/r - 5)
c) at flat section, in vertical:
N - mg = 0
N = mg