Zaid Berjis

PhysicsLesson 1 of 18About 35 minutes

What a force is, and how to draw one

Every change in motion has a cause. A ball that was sitting still starts to roll, a sliding puck comes to rest, a car turns a corner: in each case something pushed or pulled. This lesson gives that push or pull a name, a unit and a way to draw it.

By the end of this lesson you can

  • describe the three ways a force can change an object's motion;
  • use the newton, the SI unit of force, and convert from pounds;
  • tell contact forces from field forces;
  • draw and label a free-body diagram for a single object.

Forces change motion

Think first

A goalkeeper dives and stops a ball that was flying toward the net. What changed about the ball's motion? What caused the change?

Compare your answer

The ball's speed dropped to zero, so its velocity changed. The cause was the push of the goalkeeper's hands on the ball. Whenever velocity changes, look for a push or a pull.

Definition

A force is a push or a pull that one object exerts on another. A force can set a resting object in motion, or change how a moving object moves.

There are only three things a force can do to an object's velocity:

  1. Start it. A kick sets a resting ball moving.
  2. Stop it. A glove brings a moving ball to rest.
  3. Turn it. A bat sends a ball off in a new direction.

Starting, stopping and turning are all changes in velocity, and a change in velocity over time is an acceleration:

$$\vec a = \frac{\Delta \vec v}{\Delta t}$$

So the short version is: forces cause accelerations. You will make that statement exact with Newton's second law in a later lesson.

Three ways a force changes motion

Interactive
\(\vec F\)
\(\vec v\)

Scroll sideways to see the whole demo, or turn your phone sideways.

Try this

  1. Choose (a), then press Go. Watch the blue force arrow and the black velocity arrow.
  2. Repeat with (b) and (c). In each case, notice that the force arrow appears only while something touches the ball.
  3. In (c), does the force point the way the ball was moving, or the way it ends up moving? (Neither: it points the way the velocity changes.)

Measuring force: the newton

The SI unit of force is the newton (N), in honor of Isaac Newton. A force of 1 N acting alone on a 1 kg object makes it speed up by 1 m/s every second:

$$1\ \text{N} = 1\ \text{kg}\cdot\text{m/s}^2$$

A newton is a small force. Holding a 100 g apple in your palm takes about 1 N. The weight of an object is the size of the gravitational force Earth exerts on it, so weight is a force and is measured in newtons too.

In the United States, forces are often given in pounds (lb). The conversion is

$$1\ \text{lb} \approx 4.448\ \text{N} \qquad 1\ \text{N} \approx 0.225\ \text{lb}$$

Feel one newton: a spring scale

Interactive
Tap a mass to hang it on the scale:
Reading:
The reading is the weight of the mass: \(F_g = mg\).

Scroll sideways to see the whole demo, or turn your phone sideways.

Try this

  1. Hang each mass and read the scale. Which mass weighs almost exactly 1 N?
  2. Compare 100 g and 1 kg. How many times larger is the reading? What does that suggest about weight and mass?

Quick check

A suitcase weighs 15.0 lb. What is its weight in newtons?

Show solution

\(15.0\ \text{lb} \times 4.448\ \dfrac{\text{N}}{\text{lb}} = 66.7\ \text{N}\)

Contact forces and field forces

Most forces you notice in daily life need touching. You push a door, a rope pulls a sled, the floor holds you up. These are contact forces: they act only while two objects are physically in contact.

Some forces act across empty space. A dropped key speeds up toward the floor although nothing touches it. A magnet tugs a paper clip from a few centimeters away. A balloon rubbed on your sweater can lift your hair without touching it. These are field forces.

Physicists explain field forces with the idea of a field: every mass is surrounded by a gravitational field, and every charged object by an electric field. Another object placed in that field feels a force. The key falls because its mass sits in Earth's gravitational field.

A deeper look

The contact/field split is useful for everyday objects, but at the scale of atoms every contact force is really a field force. When your hand "touches" a door, the electrons in your skin and the electrons in the door repel each other through electric fields. The atoms never actually meet.

Sort the forces

Activity
Kicking a soccer ballContact force
A magnet pulling a paper clipField force
An apple falling from a treeField force
Pulling a wagon by its handleContact force
A rubbed balloon lifting your hairField force
Sitting on a chairContact force
The moon pulled toward EarthField force
Stretching a springContact force

Scroll sideways to see the whole demo, or turn your phone sideways.

Try this

For each card, decide whether the force is a contact force or a field force. Then click the card to check. Aim for eight out of eight.

Force is a vector

Give a toy car a gentle shove and it gains a little speed; shove it harder and it gains more. Shove it against its motion and it loses speed. The effect of a force depends on how big it is and which way it points, so force is a vector, written \(\vec F\).

We draw a force as an arrow:

  • it starts on the object that feels the force;
  • its head shows which way the push or pull is directed;
  • a longer arrow means a bigger force.

Push a toy car

Interactive
\(\vec F\)
Force:Car’s speed:

Scroll sideways to see the whole demo, or turn your phone sideways.

Try this

  1. Set the force and push from behind. Then double the force and push again. What happens to the change in speed?
  2. Now push from the front while the car is moving. Which way does the arrow point, and what happens to the speed?

Free-body diagrams

Real situations involve many forces at once. To make sense of them, physicists use two kinds of drawing:

  • A force diagram shows all the forces in a situation, on all the objects involved.
  • A free-body diagram singles out one object and draws just the forces exerted on it.

The free-body diagram is the one you will use to solve problems. Forces that the object exerts on other things are left out, because they cannot change the object's own motion.

A toy car rolls into a book

Interactive
\(\vec F_{\text{book on car}}\)
\(\vec F_{\text{car on book}}\)
\(\vec F_{\text{friction}}\)

Scroll sideways to see the whole demo, or turn your phone sideways.

Try this

  1. Press Run with Show forces on. At the moment of contact, two arrows appear: the book pushing the car, and the car pushing the book.
  2. Turn on Car only (free-body). Which arrow disappears, and why?

How to draw a free-body diagram

  1. Pick one object and sketch it alone, as a small box or a point. Leave its surroundings out of the picture.
  2. Find its forces. Near Earth, gravity always acts. Then look for everything in contact with the object (floors, strings, hands, the air) and give each one a force.
  3. Draw the arrows outward from the middle of the box, each aimed the way its force pushes or pulls, with lengths that match the sizes.
  4. Name each arrow, for example \(\vec F_g\) for gravity or \(\vec F_{\text{rope}}\).

Worked example 1

A child pulls a wagon along a flat sidewalk using a handle that points up at 35° above the horizontal. Earth pulls down on the wagon with 150 N, the handle pulls with 70 N, and the sidewalk pushes up with 110 N. Draw the free-body diagram of the wagon.

  1. Isolate the wagon. Draw it as a small box. The child and the sidewalk are not drawn; only their forces on the wagon will appear.
  2. List the forces on the wagon. Gravity (150 N, down), the handle (70 N, along the handle), and the sidewalk (110 N, straight up). We ignore friction in this example.
  3. Draw the arrows from the center. Gravity points straight down and is the longest. The sidewalk force points straight up and is a little shorter. The handle force points up and to the right at 35° and is about half as long as gravity.
  4. Label and check. Every arrow starts on the wagon and has a label. No force exerted by the wagon (such as the wagon pulling on the handle) appears.
    35° sidewalk, 110 N gravity, 150 N handle, 70 N

Worked example 2

A ceiling lamp hangs at rest from a single cord. Draw its free-body diagram and say how the two arrows compare.

  1. Isolate the lamp and list what acts on it. Earth pulls it down (gravity). The only thing touching it is the cord, which pulls up.
  2. Draw the arrows. \(\vec F_g\) points straight down from the center, and \(\vec F_{\text{cord}}\) points straight up.
  3. Compare the lengths. The lamp is at rest and stays at rest, so nothing is changing its motion. The two forces must be equal in size, so the arrows have the same length. (You will see why in the lesson on Newton's first law.)

Check yourself

Question 1

Which of these is a field force?

  1. Friction slowing a sliding box
  2. A magnet pulling a steel nail toward it
  3. A rope pulling a bucket up a well
  4. Your hand pushing a door open
Show solution

The magnet acts on the nail without touching it, so it is a field force. The other three need contact.

Question 2

A climbing rope is rated to hold 250 N without stretching too much. What is that in pounds?

Show solution

\(250\ \text{N} \times 0.225\ \dfrac{\text{lb}}{\text{N}} \approx 56.2\ \text{lb}\) (or \(250 \div 4.448 = 56.2\)).

Question 3

A dog pulls a sled across snow with a rope. Which force does not belong in the free-body diagram of the sled?

  1. Earth's gravitational pull on the sled
  2. The rope's pull on the sled
  3. The sled's pull on the rope
  4. The snow's upward push on the sled
Show solution

The sled's pull on the rope acts on the rope, not on the sled. A free-body diagram shows only forces acting on the chosen object.

Question 4

You hold a book still by pressing it flat against a wall with your hand. Draw the free-body diagram of the book. (Hint: there are four forces.)

Show solution

Gravity pulls the book down. Your hand pushes it toward the wall. The wall pushes back on the book, away from the wall. Friction from the wall acts upward on the book and stops it from sliding down. The two horizontal arrows have the same length, and so do the two vertical arrows.

Question 5

A curling stone slides north along the ice. A player's broom nudges it so that it curves off toward the east. Which of the three effects of a force is this? Is the broom's push a contact force or a field force?

Show solution

The force changed the direction of the motion (it "turned" the stone), so the stone accelerated. The broom touches the stone, so it is a contact force.

Summary

  • A force is a push or pull by one object on another. It can start, stop or turn an object, and each of these is an acceleration.
  • Forces are measured in newtons: \(1\ \text{N} = 1\ \text{kg}\cdot\text{m/s}^2\). One pound is about 4.448 N.
  • Contact forces need touching; field forces such as gravity and magnetism act across space.
  • Force is a vector. A free-body diagram picks out a single object and draws every force on it, and nothing else, as a labeled arrow.

Finished?

Mark the lesson as complete to keep track of your progress. Your progress is saved in this browser only.