← Weight, mass and free-body diagrams

Net force from a free-body diagram

Demi pushes a dresser over a bedroom floor. Its free-body diagram carries four arrows with sizes: the force from Demi, 90 N rightward; friction, 55 N leftward; the weight, 400 N down; the normal force, 400 N up.

force from Demi: 90 Nfriction: 55 Nweight: 400 Nnormal force: 400 N
The dresser's diagram, sizes and all.

All four act at once. What single net force do they amount to?

Work one line at a time: the up-down line first, then the left-right line.

Up against down: 400 N up and 400 N down. Equal sizes, opposite directions: they cancel, and the vertical net is zero.

weight: 400 Nnormal force: 400 Nequal and opposite: the vertical net is zero
The vertical line: 400 N up against 400 N down. They cancel.

Left against right: 90 N rightward against 55 N leftward.

Opposite directions subtract, and the leftover keeps the bigger force's direction:

90 − 55 = 35

So the net force on the dresser is 35 N rightward.

net force: 35 N
The horizontal leftover: 35 N rightward is the net force.

A hanging planter's diagram shows a tension of 18 N up and a weight of 11 N down. Enter the size of the net force on the planter in N.

tension: 18 Nweight: 11 N

A wagon's diagram shows a 40 N force rightward and 26 N of friction leftward. Which direction is the net force?

force from the handle: 40 Nfriction: 26 N

A recycling bin is pushed leftward: its diagram shows a 60 N weight down, a 60 N normal force up, 22 N from Clara leftward, and 9 N of friction rightward. Enter the size of the net force in N.

force from Clara: 22 Nfriction: 9 Nweight: 60 Nnormal force: 60 N

State both parts every time: the size and the direction.

When one line cancels, the net force is simply the other line's leftover.

Treat each line separately. Equal and opposite forces cancel; unequal opposite forces subtract, and the leftover keeps the bigger force's direction. State the net force's size and its direction.

Find the net force on Demi's dresser: 90 N rightward from Demi, 55 N of friction leftward, a 400 N weight down, and a 400 N normal force up.

Write down the vertical forces:

400 N up, 400 N down

Equal sizes, opposite directions: the vertical net is zero.

Write down the horizontal forces:

90 N rightward, 55 N leftward

Subtract, and keep the bigger force's direction:

90 − 55 = 35

The net force on the dresser is 35 N rightward.

A floor lamp is slid over a very smooth floor: a 30 N weight down, a 30 N normal force up, and an 8 N force from Yusuf rightward. The floor is so smooth that friction is too small to count. Find the net force.

Write down the vertical forces:

30 N up, 30 N down

Equal and opposite: the vertical net is zero.

Write down the horizontal forces:

8 N rightward, and nothing leftward

The net force on the lamp is 8 N rightward.

Your turn

A loaded cart's diagram shows 250 N down, 250 N up, a 75 N pull rightward, and 31 N of friction leftward. What is the net force on the cart?

pull: 75 Nfriction: 31 Nweight: 250 Nnormal force: 250 N

A bucket hangs from a rope: its diagram shows 52 N of tension up and a 38 N weight down. Enter the size of the net force on the bucket in N.

tension: 52 Nweight: 38 N

A desk's diagram shows 300 N down, 300 N up, 45 N rightward, and 45 N leftward. Enter the size of the net force on the desk in N.

force: 45 Nforce: 45 Nweight: 300 Nnormal force: 300 N