The figure below shows a constant force

In the figure below we have

The figure below shows a more general case where the force is not constant and changes with time. Here it is necessary to evaluate an integral between the initial position of the particle (

We can calculate the instantaneous power

A particle of mass

In the case where energy is conserved and there is no friction,

Let's look at the special case where we have a mass and spring, as shown below. Here we define

The negative sign in the above two equations means that the force exerted by the spring (as it is stretched or compressed) is in the direction opposite to the spring displacement

In the above two equations it is assumed that the orange block is moving slow enough so that acceleration can be neglected. Thus, the force

But whether or not the block is accelerating, the spring always exerts a force in the opposite direction of the spring displacement. This means that a spring always wants to return to its original position.

Let's now consider a rigid body rotating about a fixed point (axis) at

Where:

To calculate the work done we must evaluate the following integral between an initial rotation angle

The instantaneous power is given by

The instantaneous kinetic energy of rotation is given as

where

In the case where energy is conserved and there is no friction,

The main advantage of using Work and Energy methods is that it allows you to easily find the velocity of a body or system of bodies knowing how much "work" went into the system (provided energy is conserved, and there are no frictional losses). It avoids much of the effort in drawing free body diagrams and determining the direction of forces, etc.

For example, if a roller coaster rolls down a track and falls a vertical distance

Return to

Return to

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