# Kinetic Energy of a mass moving in horizontal circle

• Serendipitydo
In summary, the question involves finding the kinetic energy of a mass moving in a circular path with a radius of 24.6cm and a centripetal force of 96.5N. After some calculations using the equations Fc=mv^2/r and Ek=0.5mv^2, the correct answer is determined to be 11.9J.

## Homework Statement

A mass moves in a circular path that has a radius of 24.6cm on a horizontal frictionaless surface. If the centripetal force acting on the mass is 96.5N, what is the kinetic energy of the mass?
r=0.246m
Fc=96.5N

## Homework Equations

He told us to use these and "play around with them":
Fc=mv2/r
Ek=0.5mv2

## The Attempt at a Solution

I have not a clue as to how to even begin this one. Maybe use the idea that acceleration centripetal=force centripetal(minus mass)? So use:
ac=v2/r
96.5N=v2/0.246m
v2=392m/s
v=19.8m/s

Fc=mv2/r
96.5N(0.246m)=m(19.8m/s)2
m=0.0605kg

Ek=0.5mv2
Ek=0.5(0,0605kg)(392m^2/s^2)
Ek=11.9J

Or am I completely and irrevocably lost?

This has been staring me in the face for a while...

I now think I have the solution. Look at your two equations, and look what they have in common. Once you find one, you can use it to find the Kinetic Energy of that mass. Good Luck!

Just to update, I got that question correct. In the solution the teacher showed us, he combined the two formulas and got the same answer.

## 1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is dependent on both the mass and velocity of the object.

## 2. How is kinetic energy related to a mass moving in a horizontal circle?

In a horizontal circle, the object is constantly changing direction, which means it is constantly accelerating. This acceleration causes a change in the object's velocity, and therefore, its kinetic energy.

## 3. What is the formula for calculating the kinetic energy of a mass moving in a horizontal circle?

The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

## 4. Does the kinetic energy of a mass moving in a horizontal circle remain constant?

No, the kinetic energy of a mass moving in a horizontal circle is constantly changing as the object's velocity changes due to the acceleration caused by the circular motion.

## 5. How does the radius of the circle affect the kinetic energy of a mass moving in a horizontal circle?

The radius of the circle does not directly affect the kinetic energy of the object. However, it does impact the object's velocity, which in turn affects its kinetic energy. A smaller radius will result in a higher velocity and therefore, a higher kinetic energy, while a larger radius will result in a lower velocity and a lower kinetic energy.

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