Question

A solid uniform cylinder of mass 4.1 kg and radius 0.057 m rolls without slipping at a speed of 0.79 m/s. What is the cylinder’s total kinetic energy?

Answer 1

The cylinder’s total kinetic energy is 1.918 J.

Step-by-step explanation:

Given that,

Mass = 4.1 kg

Radius = 0.057 m

Speed = 0.79 m/s

We need to calculate the linear kinetic energy

Using formula of linear kinetic energy

`K.E_(l)=(1)/(2)mv^2`

`K.E_(l)=(1)/(2)*4.1*(0.79)^2`

`K.E_(l)=1.279\ J`

We need to calculate the rotational kinetic energy

`K.E_(r)=(1)/(2)* I\omega^2`

`K.E_(r)=(1)/(2)*(1)/(2)* mr^2*((v)/(r))^2`

`K.E_(r)=(1)/(4)* m* v^2`

`K.E_(r)=(1)/(4)*4.1*(0.79)^2`

`K.E_(r)=0.639\ J`

The total kinetic energy is given by

`K.E=K.E_(l)+K.E_(r)`

`K.E=1.279+0.639`

`K.E=1.918\ J`

Hence, The cylinder’s total kinetic energy is 1.918 J.