Question

A 3.00 cm diameter coin rolls up a 30.0 degree incline plane. The coin starts with an initial angular speed of 60.0 rad/s in a straight line without slipping. How far does it roll up the incline?

Answer 1

The coin roll up to 11.57 cm at 30° incline plane.

Step-by-step explanation:

Given that,

Diameter = 3.00 cm

Angle = 30.0 °

Angular speed = 60.0 rad/s

We need to calculate the length

Using conservation of energy

`(1)/(2)mv^2+(1)/(2)I\omega^2=mgh`

`(1)/(2)mr^2\omega^2+(1)/(2)*(0.4mr^2)*\omega^2=mgl\sin\theta`

Put the value into the formula

`(1)/(2)*(1.5*10^(-2))^2*(60.0)^2+(1)/(2)*0.4*(1.5*10^(-2))^2*(60.0)^2=9.8* l\sin30`

`l\sin30=(0.567)/(9.8)`

`l=2*(0.567)/(9.8)`

`l=0.1157\ m`

Hence, The coin roll up to 11.57 cm at 30° incline plane.