A small cube (m=0.330 kg) is at a height of 339 cm up a frictionless track which
ID: 1266528 • Letter: A
Question
A small cube (m=0.330 kg) is at a height of 339 cm up a frictionless track which has a loop of radius, R = 37.29 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.
http://imgur.com/WFGpUKZ
part 1 answer : 7.20 m/s
A uniform solid cylinder (m=0.330 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.
http://imgur.com/lZF0TdJ
Explanation / Answer
1) conservation of energy
0.5mU^2 + mgH=mg(2R)+0.5mV^2
U=0
0.33*9.8*3.39-0.33*9.8*(2*0.3729) =0.5*0.33*V^2
V=7.199=7.2m/s
2)
again in rolling friction does no work so energy is conserved.this will also include rotational kinetic energy which is (0.5*I*w^2) where I is moment of inertia of solid cylinder which is m*r^2/2 .and since this is rolling w=V/r
mgH=mg(2R)+0.5*m*V^2 +0.5(m*r^2/2)*((V/r)^2)
V^2=(g*(H-2R))/(0.5+0.25) =34.55
V=5.877m/s