# Calculus based physics - Energy

• XodoX
In summary: This will help you set up an equation that you can solve for the kinetic energy of the block at the given point.
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## Homework Statement

As a particle moves along the x-axis it is acted upon by a single conservative force given by Fx=(22-2.0x)N where x is in m. The potential energy associated with this force has the value +40 J at the origin (x=0). What is the value of the potential energy at x=4 m?

## The Attempt at a Solution

Well, you have to move it so that it is Fx= 2xdx - 20dx ( -dU/dx ) so you have this equation. Then I integrated it and got x^2-20x+C... C is 40 in this case, so you have x^2-20x+40. Since it says potential energy at x=4, I plugged in the 4 and got 4^2-20*4+40= -24. That's not correct, though.

## Homework Statement

A spring (k=300N/m) is placed in a vertical position with its lower end supported by a horizontal surface. A 1.5 kg block that is initially 0.10m above the upper end of the spring is dropped from rest onto the spring. What is the kinetic energy of the block at the instant it has fallen 0.20m ( compressing the spring 0.10m) ?

## Homework Equations

1/2kxi2=Ei=mghf - energy conservation

## The Attempt at a Solution

No idea. This equation above is a guess. I think it should be this one. If it is, you probably have to solve it for something, but I don't know. Solve for k ?

For the second question:

You're on the right track thinking about conservation of energy. What will define the energy of the system at the moment the block is dropped? What will define the energy of the system after it has dropped and compressed the spring?

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

Potential energy is the energy that an object possesses due to its position or configuration, while kinetic energy is the energy an object possesses due to its motion. In other words, potential energy is stored energy, while kinetic energy is energy in motion.

## 2. How is work related to energy in calculus-based physics?

In calculus-based physics, work is defined as the force applied to an object multiplied by the displacement of the object in the direction of the force. This work done on an object is directly related to the change in the object's energy.

## 3. Can energy be created or destroyed?

According to the law of conservation of energy, energy cannot be created or destroyed. It can only be transferred from one form to another. In calculus-based physics, this concept is often demonstrated through the conservation of mechanical energy in systems.

## 4. How is energy measured in calculus-based physics?

In calculus-based physics, energy is measured in joules (J). One joule is defined as the amount of work done by a force of one newton over a distance of one meter.

## 5. What is the relationship between force and energy in calculus-based physics?

In calculus-based physics, force and energy are related through the work-energy theorem, which states that the work done by a force on an object is equal to the change in the object's kinetic energy. This means that the greater the force applied, the more work is done, resulting in a greater change in energy of the object.

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