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

Answer:

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

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

$\dfrac{1}{2}mv^2+\dfrac{1}{2}I\omega^2=mgh$

$\dfrac{1}{2}mr^2\omega^2+\dfrac{1}{2}\times(0.4mr^2)\times\omega^2=mgl\sin\theta$

Put the value into the formula

$\dfrac{1}{2}\times(1.5\times10^{-2})^2\times(60.0)^2+\dfrac{1}{2}\times0.4\times(1.5\times10^{-2})^2\times(60.0)^2=9.8\times l\sin30$

$l\sin30=\dfrac{0.567}{9.8}$

$l=2\times\dfrac{0.567}{9.8}$

$l=0.1157\ m$

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