Question

How much work is done if you push a 200 N box across a floor with a force of 50 N for a distance of 20m

Answer 1

Answer: 1000 J

The Work $W$ done by a Force $F$ refers to the release of potential energy from a body that is moved by the application of that force to overcome a resistance along a path.  

It should be noted that it is a scalar magnitude, and its unit in the International System of Units is the Joule (like energy). Therefore, 1 Joule is the work done by a force of 1 Newton when moving an object, in the direction of the force, along 1 meter:  

$1J=(1N)(1m)=Nm$  

Now, when the applied force is constant and the direction of the force and the direction of the movement are parallel, the equation to calculate it is:  

$W=(F)(d)$ (1)

When they are not parallel, both directions form an angle, let's call it $\alpha$. In that case the expression to calculate the Work is:  

$W=Fdcos{\alpha}$ (2)

For example, in order to push the 200 N box across the floor, you have to apply a force along the distance $d$ to overcome the resistance of the weight of the box (its 200 N).  

In this case both (the force and the distance in the path) are parallel, so the work $W$ performed is the product of the force exerted to push the box $F=50N$ by the distance traveled $d$. as shown in equation (1).

Hence:

$W=(50N)(20m)$  

$W=1000Nm=1000J$ >>>>This is the work