# Kinetic energy of an object sliding down a sphere

• bob1256
In summary, the conversation discusses a particle of mass m sliding down a fixed, frictionless sphere of radius R. The initial conditions are that the particle starts at rest at the top of the sphere and theta represents the amount of degrees down the side of the sphere that the particle has slid. The conversation then asks for various quantities to be determined in terms of m, g, R, and theta.i. The kinetic energy of the particle can be determined by looking at the potential energy of the particle. However, the height is not explicitly known, so further calculations may be necessary.ii. The centripetal acceleration of the mass can be determined using the formula a = v^2 / r, where v is the velocity of the particle
bob1256
A particle of mass m slides down a fixed, frictionless sphere of radius R. starting from rest at the top. Theta is the amount of degrees down the side of the sphere that the particle has slid...

a. In terms of m, g, R. and theta, determine each of the following for the particle while it is sliding on the
sphere.
i. The kinetic energy of the particle
ii. The centripetal acceleration of the mass

iii. The tangential acceleration of the mass

b. Determine the value of theta at which the particle leaves the sphere.Any help would be extremely helpful...

Welcome to PF, bob. Before we can help, you should show your attempts at solving it.

Start by looking at the kinetic energy, and write that in terms of the potential energy. careful...you don't know the height explicitly.

## 1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion.

## 2. How is kinetic energy calculated?

Kinetic energy is calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

## 3. What is meant by an object sliding down a sphere?

When an object slides down a sphere, it means that the object is moving along the surface of the sphere due to the force of gravity.

## 4. Does the shape of the sphere affect the kinetic energy of the object?

Yes, the shape of the sphere does affect the kinetic energy of the object. The kinetic energy is dependent on the mass and velocity of the object, but the shape of the sphere can impact the velocity of the object as it slides down.

## 5. How does friction play a role in the kinetic energy of an object sliding down a sphere?

Friction can decrease the kinetic energy of an object sliding down a sphere by converting some of the energy into heat. The amount of friction depends on the material of the sphere and the surface of the object, and can be calculated using the coefficient of friction.

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