# Kinetic Energy, Potential Energy, Work

• jskellington
In summary, the conversation discusses a question involving a slingshot and an object with given mass, angle, and height. The equations used to solve the problem include the conservation of energy and the work of the spring. The individual's main question is whether it is correct to substitute the work of the spring for the initial kinetic energy, and when it is appropriate to do so. The suggestion is made to simply use spring energy and kinetic energy instead.
jskellington
Hi! So this is a more general question about a question that I have already solved but I'm still confused and it seems like I'm missing the concept here.

## Homework Statement

I'll try to recall the question as best I can from memory. A person is standing at a certain height h and shoots an object with some mass m at some angle z with a slingshot that acts as a spring with a k of k. The question asked for the velocity after the slingshot was released.

## Homework Equations

Kf + Ugf = Ki + Ugi
1/2mvf^2 + mgy = 1/2mvi^2 + mgh
Ws = 1/2 kxi^2 + 1/2 kxf^2

## The Attempt at a Solution

So basically what I did was plug in the values to find the work of the spring on the ball which I found to be 1/2kd^2. My main question is whether or not it is correct to substitute this value into the first equation above for Ki, the initial kinetic energy. This provided the correct answer and I found velocity by solving for Vf. I'm not sure if this makes any sense because I'm pretty confused myself. Thanks for any assistance.

Wouldn't it be easier to just use
spring energy -> kinetic energy
.5kx^2 = .5mv^2

I suppose it would be--I think I've come up with my actual question now. When is it correct to substitute Work for Kinetic energy. Should I always substitute it in for Ki in the first equation and if it is vertical displacement, simply add mgh?

Sounds okay. I personally wouldn't bother with a W at all.
I think in terms of energy before = energy after
and put in whatever kinds of energy there are in each case.

## 1. What is the difference between kinetic energy and potential energy?

Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object has due to its position or state. Kinetic energy is directly proportional to an object's mass and the square of its velocity, while potential energy is determined by factors such as an object's height, mass, and the strength of a force acting upon it.

## 2. How do you calculate the total mechanical energy of an object?

The total mechanical energy of an object is the sum of its kinetic energy and potential energy. This can be calculated using the equation E = KE + PE, where E is the total mechanical energy, KE is the kinetic energy, and PE is the potential energy.

## 3. What is the relationship between work and energy?

Work is the transfer of energy from one form to another. When work is done on an object, energy is transferred to that object and it gains either kinetic or potential energy. Similarly, when an object does work, it loses energy and its kinetic or potential energy decreases.

## 4. How is work related to force and displacement?

Work is defined as the product of the force applied to an object and the displacement of that object in the direction of the force. This can be expressed as W = Fd, where W is work, F is force, and d is displacement. Work is measured in joules (J).

## 5. Can energy be created or destroyed?

According to the Law of Conservation of Energy, energy cannot be created or destroyed, it can only be transformed from one form to another. This means that the total amount of energy in a closed system remains constant. For example, potential energy can be converted into kinetic energy, but the total amount of energy in the system will not change.

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