Question

A solid cylinder and a hollow cylinder with the same mass and radius are released at the top of a ramp.

Which will have the slower speed at the bottom of the ramp and why?

using appropriate equations and words

Answer 1

Solution) Mass m

Radius R

Solid cylinder , Vs = ?

mgh = (1/2)(m)(Vs^2) + (1/2)(I)(w^2)

V = rw

w = (V/r)

Here V = Vs

I = (1/2)(m)(R^2)

mgh = (1/2)(m)(Vs^2) + (1/2)(1/2)(m)(R^2)(Vs/R)^2

mgh = (3/4)(m)(Vs^2)

Vs^2 = (4gh/3)

Vs = (4gh/3)^(1/2)

Vs = 1.15(gh)^(1/2)

Hollow cylinder , Vh = ?

mgh = (1/2)(m)(Vh^2) + (1/2)(I)(w^2)

I = mR^2

mgh = (1/2)(m)(Vh^2) + (1/2)(m)(R^2)(Vh/R)^2

mgh = m(Vh^2)

Vh = (gh)^(1/2)

Vs > Vh so solid cylinder reaches first .