Question

Pls explain results, ty!

You roll different cylindrical pipes (hollow cylinders) down an incline plane. They have different masses, different radii, and different lengths but they are all released from the same height. Will they arrive at the bottom the same time or different times?

Show this with calculations. Hint: Use conservation of energy (compare the total energy at the top and the bottom of the incline, assuming H as the height, M as the mass and R as the radius of the cylinder) and find the velocity of the cylinder as it reaches the bottom. Does it matter if you now replace M or R with different values?

Answer 1

hollow cylinders  

total energy at top = total energy at lowest point

mgh =1/2*m*v^2 + 1/2*I*w^2

w = v/r  

I = mr^2 for   hollow cylinders so

mgh = 1/2*m*v^2 + 1/2* mr^2 * (v/r)^2

v =  √gh m/s  

so speed at bottom doesn't depends on cylinder's M as the mass and R it only depends on only height of the incline plane so

Does it matter if you now replace M or R with different values? => NO

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