Lesson 19: Net Force

Up to this point we have been focusing on situations that involve only one force acting on an object.

This is what we do when we look at net force.

There are several common forces acting on objects that you need to memorize:

Fg = force due to gravity

Fa = applied force

FN = normal force

FNET = net force

Ff = force due to friction

To keep track of how all these forces are affecting a single object, it is a good idea to draw a free body diagram.

Quite often we are able to ignore many of the forces that cancel each other out.

FNET = Fa + Ff

Example 1: I want to push my tarantula’s 8.7kg cage across the table. I push with 29N of force, and there is a force due to friction of 8N between the table and the cage. Determine how much the cage will accelerate.

First, draw a free body diagram.

Since nothing is happening along the y-axis, we can ignore the Fg and FN forces.

FNET = Fa + Ff

= 29N + -8N

FNET = 21N

I had to make the friction a negative force because it is pointing in the direction opposite to the applied force.

When you want to calculate the acceleration of an object, always use the net force acting on it.

FNET = ma

a = FNET / m

= (21N) / (8.7kg)

a = 2.4 m/s2

The Elevator Question

The concept of net force becomes a bit more complicated when you examine a complex system like an elevator going up and down.

When the elevator is accelerating up, what would happen to your weight?

What would happen to your apparent weight if the elevator started to accelerate down?

Let’s look at how we would actually figure out some numbers for this type of question by looking at an example.

Example 2: You are standing on a scale in an elevator. You have a mass of 75kg. Determine what a scale would show as your “apparent” mass (in kilograms) if…

a) the elevator starts to accelerate upwards at 3.0m/s2.

We need to think of the net force as the force pushing down on the scale causing it to give a reading.

FNET = Fg + Fa

FNET = Fg + Fa

= mg + ma <- since mass is common, I’ll factor it out

= m (g + a)

= 75kg (-9.81m/s2 + -3.0m/s2) <- both are negative

= 75kg (-12.81m/s2)

FNET = -9.6e2 N

FNET = mg

m = FNET / g

= (-9.6e2 N) / (-9.81m/s2)

m = 98 kg

So a regular scale thinks you weigh 98 kg!

b) the elevator starts to accelerate downwards at 4.0m/s2.

We’ll handle this part of the question the same way.

FNET = Fg + Fa

= mg + ma

= m (g + a)

= 75kg (-9.81m/s2 + 4.0m/s2) <- both are negative

= 75kg (-5.81m/s2)

FNET = -4.4e2 N

The scale will read...

FNET = mg

m = FNET / g

= (-4.4e2 N) / (-9.81m/s2)

m = 44 kg

So a regular scale thinks you weigh 44 kg!