A 0.0215 m diameter coin rolls up a 20.0 degree inclined plane. The coin starts with an initial angular speed of 55.2 rad/ s and rolls in a straight line without slipping. How much vertical height does it gain before it stops rolling?

The coin will reach a vertical height of 0.027 meters before it stops rolling.

Explanation:

Let suppose that coin-ground system is a conservative system and begins at a height of zero. Since the coin is experimenting a general plane motion, which is a combination of translation and rotation. By Principle of Energy Conservation we have the following model:

(1)

Where:

- Translational kinetic energy at the bottom of the incline, in joules.

- Rotational kinetic energy at the bottom of the incline, in joules.

- Gravitational potential energy at the top of the incline, in joules.

By definitions of Kinetic and Gravitational Potential Energy we expand (1):

(2)

Where:

- Momentum of inertia of the coin, in kilogram-square meters.

- Angular speed, in radians per second.

- Radius of the coin, in meters.

- Mass, in kilograms.

- Gravitational acceleration, in meters per square second.

- Height reached by the coin, in meters.

The momentum of inertia of the coin is calculated by:

(3)

Then, we expand and simplify (2):

If we know that , and , then the height reached by the coin is:

The coin will reach a vertical height of 0.027 meters before it stops rolling.

answer: 802.3 kilo joules of energy represents 191.75 kilo calorie of energy.

explanation:

energy released during combustion of one mole methane = 802.3 kilo joules

if 1 kilo joule = 0.239006   kilo calorie

then ,802.3 kilo joule will be = 802.30.239006 kilo calorie

802.3 kilo joule = 191.75 kilo calorie

hence, the energy in kilo calorie is 191.75 kilo calorie.

i just did an experiment like this in my science class. also the answer is yes, it will get separated because they are two opposites meaning if they are opposite they can not attract.

hope this .!