Question

A cylinder, starting from rest, with a mass of 0.950 kg has a radius of 5.00 cm.

a) Find the final tangential speed of a solid cylinder rolling down a 4.0 m high incline

b) Calculate the speed of the cylinder it slid down a frictionless incline without rolling.

c) Why are the speeds different?

Answer 1

here,

mass , m = 0.95 kg

radius , r = 5 cm = 0.05 m

a)

h = 4 m

let the final tangential speed be v1

using conservation of energy

m * g * h = 0.5 * m * v1^2 + 0.5 * I * w^2

m * g * h = 0.5 * m * v1^2 + 0.5 * (0.5 * m * r^2) * (v1/r)^2

m * g * h = 0.5 * m * v1^2 + 0.25 * (m ) * (v1)^2

9.81 * 4 = 0.75 * v1^2

solving for v1

v1 = 7.23 m/s

the final tangetial speed is 7.23 m/s

b)

when the cyclinder is not rolling

let the final tangential speed be v2

using conservation of energy

m * g * h = 0.5 * m * v2^2

g * h = 0.5* v2^2

9.81 * 4 = 0.5 * v2^2

solving for v2

v2 = 8.86 m/s

the final tangetial speed is 8.86 m/s

c)

as when the cyclinder is rolling

mechanical energy is also contribute in rolling motion

so, the translation kinetic energy is smaller as compared to only translation motion

so, the speeds are different