Who Feels the Bigger Push in a Crash?: Going Further 6–8

Pushes come in pairs

Press your hand flat against a wall and push. You feel the wall pushing back on your hand. Push harder, and the wall pushes back harder. You can’t push the wall without the wall pushing you.

It is the same with everything. A force is always between two things. When you step out of a small boat on Phewa Lake onto the shore, your feet push the boat backwards, and the boat pushes you forwards. That is why the boat drifts away behind you, and why it is easy to fall in if you step off too quickly.

Figure 6.1 Two pairs of pushes. Stepping off a boat, the feet push the boat backwards and the boat pushes the man forwards. Hitting a ball, the racket pushes the ball and the ball pushes the racket back. In each pair, the two forces are the same size, in opposite directions, and they act on different things.

When two things push or pull on each other, the two forces are always the same size, and they point in opposite directions. This is Newton’s third law. It is true for every pair of things, big or small, moving or still, and it is true at every moment, not just on average. The two forces are called a force pair (or an action and a reaction).

Notice something important. The two forces of a pair act on two different things: one on you, one on the boat. So they never cancel each other out. To find out what happens to the boat, look only at the forces on the boat, as you did in Adding up forces.

Activity

Push off a friend

You need: a friend about your size, a smooth floor (tiles or cement), socks, and an adult nearby.

Stand facing your friend, both in socks, an arm’s length apart, with plenty of clear space behind you both.
Put your palms flat against your friend’s palms. Your friend keeps their arms still and stiff. Only you push, gently.
Watch what happens to both of you. Then swap: your friend pushes and you keep still.
Now try it with someone much bigger than you, like a grown-up. Who slides farther?

Push gently, never suddenly, and stop if anyone starts to lose their balance.

What you should see

You both slide backwards, even when only one of you pushes. Your push on your friend has a partner: your friend’s hands push back on you, just as hard. With a grown-up, you slide back much farther than they do, although the two pushes are still equal. That is the next idea.

A tiny mosquito hits the windscreen of a bus going along the highway. Which is true?

Pick an answer to see why.

You push a heavy box across the floor. The box pushes back on you just as hard. Why can the box move at all?

Pick an answer to see why.

You will meet Newton’s third law again in Grade 9: Newton’s third law of motion.

Equal pushes, different changes

Now back to the crash. In a crash, the two vehicles push on each other. By the third law, those two pushes are always the same size. They also start at the same moment (when the two touch) and stop at the same moment (when they come apart). So both vehicles get the same push for the same time.

But the same push doesn’t do the same thing to both. You found in How much change? that the more mass a thing has, the less its motion changes:

$\text{acceleration} = \frac{\text{force}}{\text{mass}}$

So in a crash, the vehicle with less mass has its motion changed more. If the truck has nine times the mass of the car, the car’s velocity changes nine times as much as the truck’s.

Remember that velocity is speed in a particular direction Grade 8: Velocity. A car going east at 10 m/s that ends up going west at 8 m/s has had its velocity changed by 18 m/s: 10 m/s to stop, and 8 m/s more to go the other way.

Figure 6.2 A made-up head-on crash between a 1,000 kg car and a 9,000 kg truck, each going at 10 m/s, drawn to scale. During the crash they push each other equally hard (the middle row draws them pulled apart, so you can see each push ending on the thing it pushes). Afterwards they move off together the truck’s way at 8 m/s. The car’s velocity changed by 18 m/s, the truck’s by only 2 m/s.

Working it out

In Figure 6.2 the crash lasts 0.1 s, and the push between the car and the truck averages 180,000 N. You can work out what this push does to each of them in two steps.

Find the acceleration: force ÷ mass.
Multiply by the time. You learned in Grade 8 that acceleration is how much the velocity changes every second Grade 8: Acceleration, so the change in velocity = acceleration × time.

Try it on a track. The left trolley has a spring bumper, and runs at 1 m/s into the other one, which is standing still. The graph below the track shows the push on each trolley while they touch: the push on trolley 2 is drawn upwards (to the right) and the push on trolley 1 downwards (to the left).

Choose the mass of each trolley, then press Crash. Look at the two curves on the graph: are the pushes ever different in size? Then compare the changes in velocity. Try 1 kg into 4 kg, then 4 kg into 1 kg.

Trolley 1:

Trolley 2:

Biggest push on 1: 37 N ←
Biggest push on 2: 37 N →
Trolley 1 after: 0.33 m/s ←
Trolley 2 after: 0.67 m/s →
Change in velocity of 1: 1.33 m/s
Change in velocity of 2: 0.67 m/s

The pushes are equal, but trolley 1 has less mass, so its velocity changes twice as much as trolley 2’s. It bounces back.

What you should notice:

Whatever the masses, the two curves are mirror images: at every moment, the push on trolley 1 is exactly as big as the push on trolley 2, in the opposite direction.
The trolley with less mass always has the bigger change in velocity. Twice the mass, half the change; four times the mass, a quarter.
A heavier trolley makes the pushes bigger (for both), and makes the crash last a little longer.

A loaded truck of 12,000 kg and a car of 1,200 kg crash. Which statement is right?

Pick an answer to see why.

Who feels the push inside?

So who feels the bigger push in a crash? The two vehicles push on each other equally. But the people inside are a different story.

The people in a car move along with it. When the car’s velocity changes by 18 m/s in 0.1 s, the people’s velocity must change by the same amount in the same time, or they fly forward into the dashboard. So their seat belts must push them just as hard as needed to change their motion that much. In the truck, the velocity changes only 2 m/s, and the driver’s seat belt pushes far more gently.

So the honest answer to the title is: the vehicles push each other equally, but the people in the lighter vehicle feel the bigger push. This is why, in crashes between two vehicles, the people in the lighter one are hurt much more often, and why people on bicycles and motorbikes, and people walking, need the most protection on the road.

Spreading out the push

You can’t make a crash push one side harder than the other: the third law doesn’t allow it. But you can make the push smaller for both sides. Here is how.

Think about catching a hard cricket ball. A good fielder doesn’t hold their hands stiff. As the ball arrives, they let their hands move back with it. Why?

Whatever you do, the ball has to stop: its velocity has to change by the same amount. If the hands are stiff, it stops in a very short time, so the push must be big. If the hands move back with it, the stop takes longer, and a smaller push is enough.

Figure 6.3 Catching a 160 g cricket ball arriving at 20 m/s, two ways, drawn from the numbers in the example below. With stiff hands, the ball stops in 10 ms (a hundredth of a second) and the push rises to about 500 N at its biggest (320 N on average). With the hands pulled back, the stop takes 50 ms and the push rises to only about 100 N (64 N on average). Both catches stop the ball.

So: to make a crash gentler, make the stop take longer. That usually means letting something give way over a longer distance. You already do this:

When you jump down from a wall, you bend your knees as you land. Your body stops over a longer time, and the ground’s push on your feet is smaller.
A high jumper lands on a thick soft mattress, not on the ground.
A helmet has a layer of stiff foam inside that crushes in a crash, so the head stops a little more slowly.
An egg packed in a tray of soft card survives being carried home in a bag.

Why does a fielder pull their hands back while catching a fast ball?

Pick an answer to see why.

Design a softer crash

Car makers can’t change the third law, or the mass of the car that hits you. But they can design what happens at the place where the two things meet. That is engineering: using a scientific idea to solve a real problem.

In Design a hand warmer you met the loop engineers follow: set the goal, plan and build, test, and improve. The goal is written as criteria (what the design must do) and constraints (the limits it must work within).

The car’s crumple zone

The front and back of a modern car are designed to crush in a crash, while the middle part, where the people sit, is a strong, stiff cage. The front that crushes is the crumple zone. As it folds up, the car stops over a longer distance and a longer time, so the push on the car, and on the people inside, is smaller. You met crumple zones in When a crash happens, where they take away the car’s kinetic energy.

A small blue car pressed against a concrete wall in a brightly lit test hall; its front is crumpled and its airbag has inflated, while the doors and roof are undamaged — **Figure 6.4** A crash test: a small car driven into a solid wall at 56 km/h. The front has crushed by more than half a meter (54 cm), but the part where the people sit has kept its shape (all four doors still opened afterwards), and the airbag has filled to catch the driver. Photo: Calspan Corporation, National Highway Traffic Administration, Public domain

But a crumple zone can’t just be as soft as possible. Design one yourself and you will see why.

Here is the problem. A 1,200 kg car hits a concrete barrier at 50 km/h. You choose how long its crumple zone is, and how hard it is to crush (its crush force: how hard it pushes back while it is crushing). By the third law, the crumple zone pushes on the barrier and the barrier pushes on the car with this same force.

Criteria:

a.The car must stop before the crumple zone is used up. If it isn’t, the stiff cabin hits the barrier and is crushed.
b.The push on the people inside must be no more than 20 times their weight.

Constraint: the crumple zone must fit in the front of the car: no more than 80 cm.

(The 20 times is our own goal for this game. Real crash tests measure many things, such as the push on the head and chest, using crash-test dummies full of sensors.)

Change the length and the crush force, then press Crash to watch it in slow motion. During the crash, the red arrow is the barrier’s push on the car and the blue arrow the car’s push on the barrier: watch their lengths. The graph shows the push over time, and the dashed line is the most the people may feel. Can you meet both criteria? Find the shortest crumple zone that works.

Crumple zone length: 50 cm Crush force: 300 kN

Crumple zone used: 39 cm
Time to stop: 56 ms
Biggest push on car and barrier: 300 kN
Biggest push on a 60 kg person: 15,000 N
That is: 25.5 × their weight
Cabin: safe

The cabin is safe, but the stop is too hard: the push on the people is over 20 times their weight. Make the zone easier to crush, and long enough to stop the car.

What you should find:

A stiff zone (a big crush force) stops the car in a short distance and a short time, with a big push: the cabin is safe, but the people are hurt.
A soft zone (a small crush force) gives a gentle push, but it may be used up before the car has stopped. Then the cabin hits the barrier and is crushed, and unless the car was nearly stopped, the push shoots up, far higher than a stiff zone’s.
The best design is a zone that is soft enough, and long enough to stop the car in. The longer the zone, the softer it can be. With this car, a zone shorter than about half a meter can’t meet both criteria at all, whatever its crush force.
At every moment, the red and blue arrows are the same length. The design changes how big the pushes are, never which one is bigger.

Real engineers have one more problem: a car must also be safe when it is hit by a heavier car, or hits a lighter one. A car with a very stiff front is safer for the people inside it, but pushes harder on whatever it hits. So designs try to protect the people on both sides of a crash.

A story from science

The man who made cars crumple

In the early days of the motor car, people thought a safe car was a strong, stiff one. Then the stiff car stopped very suddenly, and the people inside were thrown against it.

Béla Barényi (1907–1997), born in Austria to a Hungarian father and an Austrian mother, worked on safety at the car maker Daimler-Benz in Germany from 1939. He saw the problem the other way round. He split the car into three parts: a strong, stiff cage for the people in the middle, and a front and a back that were meant to crush, slowly and in a controlled way, so the cage stopped more gently. His company patented the idea in 1952, and in 1959 the first cars built that way went on sale. Today almost every car in the world has crumple zones. Barényi was also behind other safety ideas, such as a steering column that folds up in a crash instead of being pushed into the driver’s chest.

Shields in space

The same idea protects spacecraft. In space, tiny specks of rock and old bits of rocket fly around at many kilometers a second. A speck hitting a spacecraft’s wall directly would punch a hole in it.

A round spacecraft part on a stand, with several thin sheets stacked one above another, separated by gaps and held apart by posts — **Figure 6.5** The shield of NASA’s *Stardust* probe, which flew through the dust around a comet in 2004: thin sheets with gaps between them, in front of the spacecraft. Photo: NASA, Public domain

Build and test a crash bumper

Now design one for real.

Activity

Save the egg

The problem: a toy car (or a small cardboard box on wheels) carries a raw egg as its “passenger”. It rolls down a ramp into a wall of heavy books. Design a bumper that lets the egg survive.

You need: a toy car or truck big enough to carry an egg (or a small box taped onto one), a raw egg in a small sealed plastic bag (so that a broken egg doesn’t make a mess), a board or big book for a ramp, books to prop it up and to make the wall, sticky tape, and things to make bumpers from: paper, card, drinking straws, rubber bands, a sponge, cotton wool.

Criteria: the egg doesn’t crack when the car is let go from the top of the ramp.

Constraints: the bumper may stick out no more than 5 cm in front of the car; you may use only the materials above; nothing may be fixed to the wall (all the protection must be on the car, as on a real car).

Prop up the ramp. Put the wall of books about 30 cm beyond the bottom. Seat the egg in its bag in the car, against the front, and tape it in so it can’t fall out.
First test with no bumper, from a low starting point. Each time, raise the starting point a little, until the egg cracks. Note the height. (Use a cheap egg, and put a cloth under the books.)
Now design a bumper. Draw your design first and say how it should work, using what you learned: what will make the stop take longer?
Test it from the same starting heights. Does the egg survive higher than without a bumper? Record your results in a table.
Improve your design and test again. Compare it with a friend’s design: which survives the highest start, and why?

An adult should help with the eggs. Wash your hands after touching raw egg.

What you should see

Without a bumper, the car stops almost at once when it hits the books, so the front of the car has to stop the egg just as suddenly, with a big push: it cracks even from a low start. A good bumper crushes or springs back as the car hits the wall, so the car stops over a few centimeters instead of a few millimeters, and the push on the egg is much smaller. Folded paper “concertinas” and straw frames work well: they crush slowly. A very soft bumper (a little cotton wool) is used up at once and hardly helps, just like the too-soft crumple zone. Whatever bumper you use, the books push the car exactly as hard as the car pushes the books: the bumper makes both pushes smaller by making them last longer.

Here are one class’s results (made up for this book, but typical):

Design	Highest start with the egg unbroken
No bumper	4 cm
A ball of cotton wool	5 cm
A sponge, 3 cm thick	12 cm
Paper folded into a concertina, 5 cm long	25 cm
Four straws in a square frame, 5 cm long	20 cm

In the table, why does the paper concertina do better than the cotton wool?

Pick an answer to see why.

In short

A force is always between two things. When one thing pushes or pulls another, the second pushes or pulls back on the first: the same size, in the opposite direction (Newton’s third law). The two forces act on different things, so they don’t cancel.
In a collision, the two objects push each other equally hard, for the same time.
The same push changes the motion of a small mass more: the change in velocity is in inverse proportion to the mass (half the mass, twice the change). Acceleration = force ÷ mass; change in velocity = acceleration × time.
So in a crash, the people in the lighter vehicle feel the bigger push.
To make a crash gentler, make the stop take longer: bend your knees, pull your hands back, use crumple zones, helmets and bumpers. The pushes on both sides get smaller together.
A design must meet its criteria within its constraints: a crumple zone must be soft enough, and long enough.

Questions

A boy of 30 kg on a skateboard pushes off a wall. Which force makes him move away from the wall?

Pick an answer to see why.

Two ice skaters, a 40 kg girl and an 80 kg man, stand facing each other on smooth ice and push each other apart. Which is right?

Pick an answer to see why.

a.

A car hits a buffalo standing on the road. a. Compare the force of the car on the buffalo with the force of the buffalo on the car. b. The car has a mass of 1,000 kg and the buffalo 500 kg. Whose velocity changes more, and by how many times? c. Why might the car’s front be badly damaged even though the car’s velocity changes less?

Answer

a.They are a force pair: exactly equal in size, opposite in direction. The car pushes the buffalo forwards, and the buffalo pushes the car backwards just as hard.
b.The buffalo has half the car’s mass, so the same push for the same time changes its velocity twice as much as the car’s.
c.Damage depends on how big the push is and how strong each thing is, not only on the change in velocity. A big push on a small patch of the car’s thin metal front bends it (and the crumple zone is designed to crush), even though the car’s motion changes less.

b.

In a crash test, a trolley of mass 2 kg moving at 3 m/s hits a trolley of mass 4 kg at rest. They push each other with an average force of 80 N for 0.05 s. a. Find the change in velocity of each trolley. b. The first trolley started at 3 m/s to the right. What is its velocity after the crash? c. What is the second trolley’s velocity after the crash?

Answer

a.Trolley 1: acceleration = 80 N ÷ 2 kg = 40 m/s²; change = 40 m/s² × 0.05 s = 2 m/s (to the left, the way the push on it points). Trolley 2: 80 N ÷ 4 kg = 20 m/s²; change = 20 m/s² × 0.05 s = 1 m/s (to the right).
b.It was going 3 m/s to the right and lost 2 m/s: 1 m/s to the right.
c.It was at rest and gained 1 m/s: 1 m/s to the right. (The two trolleys now move together at the same speed: they stuck together.)

c.

A student crashed trolleys of different masses into each other in the widget, and recorded the change in velocity of each (trolley 1 always runs at 1 m/s into trolley 2 at rest):

Trolley 1 (kg)	Trolley 2 (kg)	Change in velocity of 1 (m/s)	Change in velocity of 2 (m/s)
1	1	1.00	1.00
1	2	1.33	0.67
1	4	1.60	0.40
2	1	0.67	1.33
4	1	0.40	1.60

a. In each row, divide the bigger change by the smaller one, and compare it with the masses. What pattern do you see? b. Use Newton’s third law to explain the pattern. c. Predict the changes for a 2 kg trolley into a 4 kg one, and check with the widget.

Answer

a.1.33 ÷ 0.67 = 2, when one mass is twice the other; 1.60 ÷ 0.40 = 4, when one mass is four times the other; equal masses give equal changes. The ratio of the changes is always the ratio of the masses, the other way up: the trolley with less mass has the bigger change, by the same factor.
b.By the third law, the two trolleys push each other with equal forces, and for the same time (they touch and come apart together). The same force gives a smaller acceleration to a bigger mass (acceleration = force ÷ mass), so over the same time, the bigger mass gets a smaller change in velocity, smaller by exactly the ratio of the masses.
c.The masses are in the ratio 1 : 2, the same as 1 kg into 2 kg, so the changes are the same: 1.33 m/s for the 2 kg trolley and 0.67 m/s for the 4 kg one. (The widget shows this. The pushes are bigger than with 1 kg and 2 kg, but the crash lasts longer too.)

d.

On some highways, a set of plastic barrels filled with sand stands in front of the end of a concrete wall, where a car that leaves the road might hit it. When a car hits the barrels, it pushes the sand in each one out of the way, one after another, and slows down. a. Use the third law to explain what slows the car. b. Why does this hurt the people in the car less than hitting the concrete wall? c. The barrels at the front have less sand than the ones at the back. Suggest why.

Answer

a.The car pushes on the sand and sets it moving; by the third law, the sand pushes back on the car just as hard, in the opposite direction, and that backward push slows the car.
b.The car stops over a long distance (several barrels) and a long time, instead of in a few centimeters against the wall. The same change in velocity spread over a longer time needs a smaller push, on the car and on the people.
c.Each barrel’s sand pushes back harder the more sand there is (more mass to set moving) and the faster the car is going. At first the car is fastest, so the front barrels have the least sand, to keep that first push gentle. As the car slows, heavier barrels can push harder without making the push too big. (The idea came from the racing driver John Fitch, who saw a fatal crash at Le Mans in 1955, and tested his first barrels himself.)

e.

A cycle helmet maker tests two designs. Each is fixed to a head-shaped weight and dropped onto concrete from the same height. (Made-up data.)

Design	Foam thickness	Time for the head to stop	Biggest push on the head
A: hard plastic shell, no foam	0 cm	0.002 s	25,000 N
B: shell with stiff foam	3 cm	0.008 s	6,000 N

The criteria for a safe helmet: the biggest push on the head must be under 10,000 N. The constraints: it must be light and not too big to wear. a. Which design meets the criteria? b. Explain, using what you know about crashes, why B gives a smaller push. c. Someone suggests making the foam 10 cm thick to do even better. Give one reason for and one against.

Answer

a.Design B (6,000 N is under 10,000 N). Design A, at 25,000 N, fails.
b.The head has to stop either way: its velocity changes by the same amount. The foam crushes as the head hits, so the head stops over a longer time, 0.008 s instead of 0.002 s. A stop that takes longer needs a smaller push. The concrete still pushes the helmet exactly as hard as the helmet pushes the concrete, but both pushes are smaller.
c.For: thicker foam can crush over a longer distance, so the stop would take even longer and the push would be smaller. Against: a 10 cm helmet would be big and heavy, and break the constraints; nobody would want to wear it, and a helmet that isn’t worn protects nobody. (Also, foam that is too soft is used up, like a too-soft crumple zone, so thickness alone isn’t enough.)

f.

A small meteorite falls straight down and hits the ground. a. Name the force pair at the moment it hits. b. The ground (the Earth) has an enormous mass. What happens to the Earth’s motion? c. A spacecraft engineer wants to protect a space station from small, fast specks of rock. Using the third law, explain why a thin sheet a few centimeters in front of the wall protects it better than making the wall itself a little thicker.

Answer

a.The meteorite pushes down on the ground; the ground pushes up on the meteorite, equally hard.
b.The Earth gets the same push as the meteorite, for the same time, so its velocity does change, but by an amount far too tiny to notice, because its mass is so huge. The meteorite’s velocity changes enormously: it stops.
c.When the speck hits the thin sheet, the sheet and the speck push each other so violently that both shatter into a spray of tiny pieces. The spray spreads out in the gap, so when it reaches the wall, its push is spread over a much bigger area and a longer time. A thicker wall alone would take the whole push of the speck on one tiny spot, all at once, and could still be punched through.

Where to go next

Why Does a Rolling Ball Stop? Balanced and unbalanced forces, and how a net force changes a thing’s motion: the rule you used here.
Why Is Speeding So Dangerous? The faster a thing moves, the more energy it carries into a crash, and the farther it goes before its brakes can stop it.
How Can Something Push Without Touching? Magnets, electric charges and gravity push and pull across empty space, and they come in pairs too.