# Kinetic Energy & Momentum of a Ball released from Spring

• Physics Person
In summary, a spring with a spring constant k is compressed 10 cm from equilibrium and releases a 100 g ball when decompressed. The ball's kinetic energy and momentum can be calculated using the equations KE = 1/2mv^2 and PEspring = 1/2kx^2. The assumption that the ball's kinetic energy is equivalent to the potential energy of the spring due to conservation of mechanical energy is correct, but a diagram is needed to determine the ball's position in relation to the spring.
Physics Person

## Homework Statement

"A spring with a spring constant "k" is compressed 10 cm from equilibrium. A ball of mass 100 g is at rest next to it. The spring then decompresses quickly back to its equilibrium position causing the ball to shoot forward. If the spring constant is 500 N/m, what is the ball's kinetic energy? And what is the ball's momentum after it is struck by the spring?"

## Homework Equations

KE = 1/2mv^2
PEspring = 1/2kx^2

## The Attempt at a Solution

I have attempted to solve this by using the conservation of mechanical energy to surmise that the kinetic energy of the ball after it is released would be equivalent to the potential energy of the spring before the ball is released. However, what is confusing me is that, after the ball is released from the spring, wouldn't its velocity be higher at first, and then gradually peter off? Thus, since kinetic energy equals 1/2mv^2, and momentum equals mv, wouldn't the kinetic energy and the momentum of the ball taper off over time, as well? So I'm not sure which moment of time they want me to find the kinetic energy and momentum for. Should I just assume it's the maximum amount of kinetic energy and momentum, right at the moment when the ball is released from the spring and starts moving?

Unless you have some information about the subsequent resisting forces, it's not possible to calculate the speed of the ball at any later time.

Physics Person said:
However, what is confusing me is that, after the ball is released from the spring, wouldn't its velocity be higher at first, and then gradually peter off?

Only if there's a force acting on it. A diagram is needed. If the ball is moving on a horizontal surface under the usual frictionless assumption, then there's no force acting to change its velocity.

Alright, I see now. But would my assumption that the kinetic energy of the ball would be equivalent to the potential energy of the spring, given by the equation PEspring = 1/2kx^2, due to conservation of mechanical energy, still be correct?

Depends on where the ball is. Imagine the ball is at a position where the spring never touches it. Then obviously the kinetic energy obtained by the ball is 0.

The kinetic energy of the ball comes from work that the spring does on the ball. The spring can only do work on the ball when it is touching the ball.

Again, a diagram is needed.

RPinPA said:
Depends on where the ball is. Imagine the ball is at a position where the spring never touches it. Then obviously the kinetic energy obtained by the ball is 0.

The kinetic energy of the ball comes from work that the spring does on the ball. The spring can only do work on the ball when it is touching the ball.

Again, a diagram is needed.
It says
Physics Person said:
ball of mass 100 g is at rest next to it.
I agree it is confusing then to refer to the spring "striking" the ball.

Physics Person said:
Alright, I see now. But would my assumption that the kinetic energy of the ball would be equivalent to the potential energy of the spring, given by the equation PEspring = 1/2kx^2, due to conservation of mechanical energy, still be correct?
Yes.

## 1. What is kinetic energy?

Kinetic energy is the energy that an object possesses due to its motion. It is calculated by the mass of the object multiplied by the square of its velocity and divided by two.

## 2. How is kinetic energy related to momentum?

Kinetic energy and momentum are both measurements of an object's motion. Kinetic energy is the energy an object possesses due to its motion, while momentum is the product of an object's mass and velocity. They are related in that both increase with an increase in velocity, but kinetic energy depends on the square of the velocity while momentum is directly proportional to velocity.

## 3. How does a spring affect the kinetic energy of a ball?

A spring can be used to store potential energy, which can then be converted into kinetic energy when the spring is released. As the spring pushes the ball forward, the ball gains kinetic energy from the stored potential energy in the spring.

## 4. What factors affect the kinetic energy of a ball released from a spring?

The kinetic energy of a ball released from a spring is affected by the mass of the ball, the velocity of the ball, and the potential energy stored in the spring. The spring constant, or how stiff the spring is, can also play a role in the transfer of energy.

## 5. How can kinetic energy be calculated from a ball released from a spring?

To calculate the kinetic energy of a ball released from a spring, you will need to know the mass of the ball, the velocity of the ball, and the spring constant. You can then use the equation KE = 1/2mv^2 to calculate the kinetic energy in joules.

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