C. Forces · ForcesNewton's First Law: Inertia and Balanced Forces
C3.3 C2.2 C2.1About 65 minutes
Learning goals- I can state Newton's first law of motion.
- I can explain everyday events, including car safety, using inertia.
- I can explain that mass is a measure of inertia.
- I can use the first law (Fnet = 0) and a free-body diagram to find an unknown force on an object at rest or moving at constant velocity.
Words to know
Newton's first law (law of inertia)
If the net force on an object is zero, the object stays at rest or keeps moving at a constant velocity (constant speed in a straight line).
inertia
An object's resistance to a change in its motion. The more mass, the more inertia.
equilibrium
The state of an object with zero net force. Static equilibrium: at rest. Dynamic equilibrium: moving at constant velocity.
mass
The amount of matter in an object and the measure of its inertia, in kilograms (kg).
The pancake law
On a Saturday morning, a teenager asleep in bed tends to stay in bed. It takes an unbalanced force (perhaps a parent, perhaps the smell of pancakes) to change that. Newton would have nodded: that is his first law of motion, also called the law of inertia.
In the last lesson you saw how Galileo discovered inertia. Newton turned it into a law that applies to every object, from hockey pucks to planets.
Newton's first law
An object at rest stays at rest, and an object in motion stays in motion at a constant velocity, unless acted on by a non-zero net force.
In symbols: if Fnet = 0, then velocity is constant (and the acceleration is zero). It works the other way too: if the velocity is constant, the net force must be zero.
What the first law really says
- An object does not need a net force to keep moving. It needs a net force only to change its velocity: to speed up, slow down or turn.
- "At rest" is just a special case of constant velocity (v = 0).
- When Fnet = 0 we say the object is in equilibrium. A book on a shelf is in static equilibrium; a car cruising at a steady 90 km/h on a straight highway is in dynamic equilibrium.
Mass measures inertia
The more mass an object has, the harder it is to change its motion. A loaded grocery cart is harder to start, stop and steer than an empty one. A fully loaded transport truck needs a much longer distance to stop than a small car at the same speed. Mass is the measure of an object's inertia.
Inertia and car safety
When a car brakes hard, the brakes and road act on the car. They do not act directly on you. Your body keeps moving forward at the car's old speed until something pushes back on it:
- A seatbelt pushes on your strong hip bones and chest and slows you with the car.
- An airbag cushions your head and chest.
- Without them, the steering wheel, dashboard or windshield would do the stopping, very suddenly.
In a rear-end collision the car is shoved forward. Your body tends to stay where it was, so your seat pushes your back forward, but your head lags behind. A properly adjusted head restraint pushes your head forward with your body and protects your neck.
Inertia also explains a loose object (a phone, a water bottle) flying forward in a sudden stop, which is why heavy items should be secured in a vehicle.
Worked exampleExample 1: The cruising car
A 1200 kg car travels at a constant 90 km/h on a straight, level highway. The road pushes forward on its drive wheels with 650 N. Find (a) the total resistive force (air resistance plus rolling friction) and (b) the normal force.
- Constant velocity in a straight line, so by the first law Fnet = 0, both horizontally and vertically.
- (a) Horizontal, forward +: 650 N + Fresist = 0, so Fresist = −650 N, which is 650 N backward.
- (b) Vertical, up +: FN − Fg = 0, so FN = Fg = mg = (1200 kg)(9.8 N/kg) = 11 760 N up (about 1.2 × 10⁴ N).
- Notice that the forward force is not "bigger than the backward force to keep the car moving". They are equal.
(a) 650 N backward. (b) About 1.2 × 10⁴ N up.
A car cruising at a steady 90 km/h: the up and down forces balance, and the forward and backward forces balance, so the net force is zero. The forward force (from the road on the driven wheels) only has to balance the resistance, not "supply the motion".Worked exampleExample 2: An elevator moving down
An 800 kg elevator car moves down at a constant 2.0 m/s. Find the tension in its cable. (Ignore friction.)
- Constant velocity, so Fnet = 0. Direction of motion (down) does not matter.
- Up +: FT − Fg = 0.
- FT = mg = (800 kg)(9.8 N/kg) = 7840 N (about 7.8 × 10³ N).
The cable tension is about 7.8 × 10³ N up, exactly equal to the elevator's weight, even though it is moving down.
Worked exampleExample 3: Explaining with inertia
You are standing on a city bus holding nothing. The bus suddenly turns left. Which way do you lurch, and why?
- Before the turn you are moving forward with the bus.
- The bus floor pushes on your feet to turn you, but friction on your feet may not be enough to turn your whole body quickly.
- By inertia your body tends to keep moving straight ahead, while the bus turns left underneath you.
- Relative to the bus, you seem to be thrown to the right. No force pushes you right; the bus is turning away from your straight-line path.
You lurch to the right relative to the bus because your body tends to keep going straight (inertia) while the bus turns left.
Just for funA curling stone is a champion of inertia. Once a curler lets it go, nothing pushes it forward, yet it can glide the length of the sheet. The players sweeping in front of it are not pushing it; they are changing the ice in front of it, and that changes how it slides and curls.
Hands-on activityInertia tricks (with care)
You need: a plastic cup, an index card or stiff playing card, a coin, a stack of 5 or 6 checkers or coins, a ruler, and a heavy book with a string.
- Coin and card: Put the card on top of the cup and the coin on the card, over the cup's opening. Flick the card sharply sideways. The coin drops into the cup. Explain: the card was pulled out quickly, so friction acted on the coin for only a very short time; the coin's inertia kept it nearly in place, then gravity pulled it down.
- Checker stack: Stack the checkers and knock the bottom one out with a quick, sharp, flat slide of the ruler. The rest of the stack drops straight down.
- Slow pull vs quick jerk: Tie a string around a heavy book, with a second string hanging from the bottom (ask a grown-up to help). Hang it from a doorknob by the top string. A slow, steady pull on the bottom string breaks the top string; a quick jerk breaks the bottom string. Do this over a cushion, keep feet clear, and use thin thread so it breaks easily. Explain in terms of inertia: with a quick jerk, the book's inertia keeps it from moving much, so the bottom string takes all the force.
Write each explanation in two or three sentences using the words inertia and net force.
Your turn
1State Newton's first law in your own words.
If the net force on an object is zero, its velocity does not change: it stays at rest, or keeps moving in a straight line at a constant speed.
2A hockey puck slides across frictionless ice at 12 m/s. Describe its motion 5 s later if no forces act horizontally.
It is still moving at 12 m/s in the same direction. With no net force its velocity stays constant.
3A 15 kg box rests on the floor. Find the normal force.
At rest, Fnet = 0: FN = mg = 15 × 9.8 = 147 N up (about 150 N).
4A snowmobile pulls a sled at a constant velocity with a tension of 240 N. What is the friction on the sled?
Constant velocity, so Fnet = 0: friction is 240 N backward (opposite the tension).
5Why is it harder to stop a loaded grocery cart than an empty one moving at the same speed?
The loaded cart has more mass, so more inertia: it resists changes in its motion more, so a bigger force (or more time) is needed to stop it.
6Explain why a head restraint protects you in a rear-end collision.
The car and seat are pushed forward suddenly. By inertia your head tends to stay where it was, so without support it would whip backward relative to your body. The head restraint pushes your head forward together with your body.
More practice: warm-up
1What is another name for Newton's first law?
2What quantity is a measure of an object's inertia?
3If an object's velocity is constant, what is the net force on it?
4Is a book resting on a shelf in equilibrium?
Yes (static equilibrium): Fnet = 0.
5Does a moving object need a net force to keep moving?
No. A net force is needed only to change its velocity.
More practice: on your own
1A 65 kg skydiver falls at a constant (terminal) speed. Find the air resistance on her.
Constant velocity means Fnet = 0, so air resistance = Fg = 65 × 9.8 = 637 N up (about 640 N).
2A 1500 kg car moves at a constant 100 km/h. Air resistance is 520 N and rolling friction is 230 N. Find the forward force from the road.
Fnet = 0, so forward force = 520 + 230 = 750 N forward. The mass and speed are not needed.
3Why does a passenger without a seatbelt in a car that brakes suddenly hit the dashboard? Explain using the first law.
The brakes exert a backward force on the car, not on the passenger. With no backward force on the passenger, by inertia the passenger keeps moving forward at the original speed until the dashboard (a much harder object than a seatbelt) stops them.
4A 300 kg crate is lowered by a crane cable at a constant speed of 0.50 m/s. Find the cable tension.
Fnet = 0: FT = mg = 300 × 9.8 = 2940 N up (about 2.9 × 10³ N).
5Explain why a tablecloth can sometimes be yanked from under dishes without moving them much.
A very fast pull means friction acts on the dishes for only a tiny time. The dishes' inertia resists the change in motion, so in that short time they barely speed up and stay nearly in place. (Smooth cloth helps by reducing friction.)
Challenge
1A 2.0 kg lamp hangs at rest from the ceiling of a train car moving at a constant 120 km/h on straight track. Does the lamp's cord hang straight down, tilt forward or tilt backward? Explain.
Straight down. The train moves at constant velocity, so the lamp does too: Fnet = 0. The only forces are gravity (down) and tension; tension must be straight up to balance. You could not tell from the lamp that the train was moving.
2A student says, "When a ball is thrown upward, there is an upward force on it until it reaches the top." Use the first law to explain the error.
Once the ball leaves the hand only gravity (and air resistance) acts. The ball keeps moving up because of inertia, not because of an upward force. The net force is down, which is why it slows down on the way up. If there were an upward force bigger than gravity, it would speed up instead.
3A 5.0 kg box is pushed across the floor at constant velocity with a horizontal force of 18 N. The pusher then doubles the push. Is the box now in equilibrium? What will happen?
Before: Fnet = 0, so kinetic friction = 18 N. With a 36 N push, friction stays about 18 N (kinetic friction does not depend on the push), so Fnet ≈ 36 − 18 = 18 N forward. The box is not in equilibrium; it speeds up.
Quiz
1. A spacecraft far from all planets and stars has its engines off and is moving at 5 km/s. Ten minutes later it will be moving:
2. Which object has the most inertia?
3. A box slides across the floor at constant velocity while being pushed with 30 N. The friction force is:
4. When a car stops suddenly, an unbelted passenger moves forward because:
5. An elevator moves up at a constant speed. Compared with the elevator's weight, the cable tension is:
6. Which situation is NOT an example of equilibrium?
Big idea: Newton's first law (C3.3): no net force means no change in velocity. Students use it with free-body diagrams (C2.2) to find unknown forces.
How to help: Talk through car-safety features (seatbelts, head restraints, securing cargo) using the word inertia. Ask: "What would happen to the passenger if nothing pushed on them?"
Common difficulties:
- Believing a moving object needs a forward net force. At constant velocity the forward force only balances resistance.
- Thinking "constant velocity" and "at rest" are different cases. Both have Fnet = 0.
- Saying "inertia pushed me forward". Inertia is not a force; the passenger keeps moving because no force stops them yet.