A small cube (m=0.650 kg) is at a height of 333 cm up a frictionless track which
ID: 1398205 • Letter: A
Question
A small cube (m=0.650 kg) is at a height of 333 cm up a frictionless track which has a loop of radius, R = 43.29 cm at the bottom. The cube starts from rest and slides freely down the ramp and around the loop. Find the speed of the block when it is at the top of the loop.
A uniform solid cylinder (m=0.650 kg, of small radius) is at the top of a similar ramp, which has friction. The cylinder starts from rest and rolls down the ramp without sliding and goes around the loop. Find the speed of the cylinder at the top of the loop.
Explanation / Answer
For the cube:
PE = KE
PE = mgh
KE = 0.5mv2
(9.8)(3.33)=0.5v2
v=8.08m/s
(8.082 - v22)0.5 = (3.33-0.4329)(9.8)
v2 = 2.92m/s
for the cylinder:
gh = 0.5mv2 + 0.5Iw2
for solid cylinder:
I = 0.5mr2
w = v/r
KEr = 0.5(0.5mr2)(v/r)2
= 0.25mv2
(9.8)(3.33) = 0.5(v12) + 0.25(v12)
v1 =6.60m/s
0.75(6.60)2 - 0.75v22 = 9.8(3.33-.4329)
v2 = 2.39m/s