#### Work and Energy

**Energy is defined as :**

- The ability to do work
- The amount of work done

If you push an object through a certain distance (

**d)**, using a force**(F)**, you can calculate the amount of work done ,**(W)**required in moving the object.
The drawing below illustrates the above mentionned variables:

WORK = Force X Distance. Note that the distance is in the same direction as the applied force.

W = F X d

W = F X d

Where F is the Force doing the "pushing" and d is the distance the object moves.

The distance and the force must be in the same direction.

In this equation, Force is measured in [N], Newtons and distance is measured in [m], meters.

The Work-Energy Equivalence states that the amount of work done is equivalent to the energy used tp achieve this work, and viceversa.

**WORK = Energy**

Measured in Joules

1 Joule = 1 Newton-meter

1 J = 1Nm

1 Joule = 1 Newton-meter

1 J = 1Nm

**Example 1:**

A shopper pushes a grocery cart with a force of 100 N continuously for 50 m.

How much energy is she using up, and how much work is she doing on the cart?

**Solution:**

**Given**: F = 100 N

d = 50 m

**Find**: W

W = F x d

= 100 N x 50 m = 5000 J

Therefore, the shopper uses up 5000 N of Energy in pushing the grocery cart.

At the same time, the work she is doing on the cart is also 5000N since **Work = Energy.**