Have you ever watched a slow-motion video of two football players colliding or a car crashing into a barrier and wondered: Who feels the bigger force?
Objects always push on each other with forces that are exactly the same size. That idea comes from Newton’s Third Law, and it is a key tool scientists and engineers use to design safer cars, helmets, and sports equipment.
In this lesson, you will learn what Newton’s Third Law says, how it applies when two objects collide in a straight line, and how those ideas help us design solutions that control or reduce damage in collisions.
When we talk about motion, we always need a reference frame. A reference frame is a point of view or location that we all agree on so we can describe how something moves. For example, you can describe a skateboard as moving to the right along the ground at a certain speed when the ground is your reference frame. If everyone uses the same reference frame, they can agree on whether the skateboard is speeding up, slowing down, or staying at a constant speed.
Engineers often describe motion along a straight line, such as a car moving forward or backward on a straight road, or a ball dropping straight down. We can choose one direction along the line as positive (for example, to the right) and the opposite direction as negative (to the left), as shown in [Figure 1]. Then we can talk about forces and motion in that single dimension: forward/backward or up/down.
The motion of an object changes (its speed or direction) when the net force on it is not zero. The net force is the sum of all forces acting on the object along our line. If an object has more mass, it is harder to change its motion. That means for the same change in motion, a larger mass needs a larger force.
For example, if you try to push a small empty cart and a large heavy cart with the same strength in the same direction, the smaller cart’s motion changes more. You might give both carts the same size horizontal push force, but the lighter one speeds up more.
So two important ideas to keep in mind are: motion is described relative to a shared reference frame, and heavier objects need larger forces to get the same change in motion.
Newton’s Third Law tells us about forces between two objects that are interacting. The law says:
For every action force, there is an equal and opposite reaction force.
This means that when object A pushes on object B, object B pushes back on object A with a force that is:
These two forces form an action–reaction pair. They always come together. You can never have just one of them by itself.
Imagine two students on skateboards facing each other in a straight line, touching hands, as shown in [Figure 2]. If they push off, the first student pushes to the left on the second student. At the same exact time, the second student pushes to the right on the first student with a force of the same size. The forces are opposite in direction but equal in size.
Here is the important part: even though the forces are equal, the students might not move the same way. If one student has much greater mass (for example, is taller and heavier), that student’s motion will change less. The lighter student speeds up more. The forces are equal and opposite, but the effects on motion are different because the masses are different.
Not every pair of forces is an action–reaction pair. For example, the push of the floor on your feet and the push of your feet on the floor are an action–reaction pair. But the push of the floor on your feet and the push of gravity on you are not an action–reaction pair, because they act on the same object (your body) and come from different objects.
A collision happens when two objects come into contact and exert strong forces on each other for a short time. In this lesson we focus only on collisions in one dimension: head-on or rear-end collisions in a straight line, or objects moving straight toward or away from each other.
Think about a small car colliding head-on with a large truck along a straight road, as shown in [Figure 3]. During the tiny fraction of a second when the car’s front and the truck’s front are squeezed together, they push very hard on each other.
According to Newton’s Third Law, the force of the car on the truck and the force of the truck on the car are:
So if the car pushes to the right on the truck with force \(F\), then the truck pushes to the left on the car with force \(F\). Both forces act at the same time during the collision.
But again, the effect on motion is different. The truck usually has much more mass than the car. Because the same size force acts on both, the car’s motion changes more. The car can experience a much larger change in speed or direction than the truck does.
This idea applies to many 1D collisions:
In every collision, you can always identify the action–reaction force pair between the two objects, even though their motions change in different ways.
To understand why different objects change motion differently even when they experience equal and opposite forces, we use the idea that the acceleration of an object depends on both the net force and the mass.
In simple terms: for the same net force, an object with smaller mass will have a greater acceleration (bigger change in speed or direction), and an object with larger mass will have a smaller acceleration.
For example, suppose two carts on a straight horizontal track collide and push on each other with the same size force of \(10 \textrm{ N}\). One cart has a mass of \(2 \textrm{ kg}\), and the other has a mass of \(5 \textrm{ kg}\). During the collision, both carts feel a force of \(10 \textrm{ N}\) in opposite directions along the track.
Even though the force is \(10 \textrm{ N}\) on each, the lighter cart’s motion changes more. It speeds up or slows down more quickly than the heavier cart. Engineers designing vehicles and safety equipment think carefully about masses, because the same collision forces can cause much larger changes in motion for smaller, lighter objects.
Newton’s Third Law might sound like it only explains what happens, but it also helps us design ways to control what happens.
During a collision, we cannot prevent the two objects from pushing on each other with equal and opposite forces. However, we can change how large those forces are by controlling how the collision happens.Engineers use two main ideas when designing solutions for collisions in one dimension:
For example, car designers use crumple zones, seat belts, and airbags. When a car moving straight forward hits a barrier, as shown in [Figure 4], parts of the car crush and bend. This does not remove the action–reaction forces between the car and the barrier; they still push on each other with equal and opposite forces. But by stretching the collision over a longer time and allowing metal to crumple and airbags to inflate, the force on the people inside can be much smaller at any moment.
You can think about it this way: when an object’s motion changes, its momentum changes. If this change happens over a very short time, the forces are very large. If we make the time longer, we can reduce the size of the force while still changing the momentum by the same amount.
Here is a simple example with numbers that shows how changing the collision time can change the average force. Imagine a small cart of mass \(1 \textrm{ kg}\) moving straight to the right at a speed of \(4 \textrm{ m/s}\). It hits a spring bumper and comes to a stop (speed becomes \(0 \textrm{ m/s}\)).
The change in velocity is from \(4 \textrm{ m/s}\) to \(0 \textrm{ m/s}\). The change in its momentum is:
\[ \Delta p = m \cdot \Delta v = 1 \textrm{ kg} \cdot (0 - 4 \textrm{ m/s}) = -4 \textrm{ kg}\cdot\textrm{m/s} \]
The negative sign just means the cart’s velocity in the positive direction decreased. If this happens in a very short time, say \(0.1 \textrm{ s}\), the average force on the cart has a large size. If the same change happens over \(0.5 \textrm{ s}\), the average force has a smaller size. So, by making collision time longer, forces can be reduced. Designers use this idea for car bumpers, helmet padding, and landing mats.
Remember, according to Newton’s Third Law, whatever force the bumper or padding exerts on the cart, the cart exerts an equal and opposite force on the bumper or padding. So designers choose materials that can safely handle those equal and opposite forces without breaking or causing injury.
Now let’s look at some clear examples of how Newton’s Third Law helps us think through and design solutions to 1D collision problems.
Example 1: Two Carts with Different Masses
Suppose you have two carts on a straight track. Cart A has mass \(1 \textrm{ kg}\) and Cart B has mass \(3 \textrm{ kg}\). Cart A rolls straight to the right and collides with Cart B, which was initially at rest.
During the short time of the collision:
By Newton’s Third Law, these forces are equal in size and opposite in direction. Because Cart A has smaller mass, its motion changes more. Cart A might slow down a lot or even bounce backward, while Cart B begins moving to the right with a smaller change in speed.
If you wanted to reduce the force that each cart feels during the collision, how could you design the bumpers? You could use softer, springier bumpers that compress more and increase the time of contact. This increases the collision time and reduces the average force on each cart, even though the action–reaction forces are still equal and opposite.
Example 2: A Student Running into a Wall
A student runs straight toward a gym wall and accidentally bumps into it. The student exerts a force on the wall. At the same time, the wall exerts an equal and opposite force on the student.
To make this situation safer, schools use padded walls in some areas. The padding increases the time during which the student’s body slows down to zero. According to Newton’s Third Law, the force the wall exerts on the student and the force the student exerts on the wall remain equal at every moment, but the padding stretches out the collision and reduces the size of the forces at each instant.
So, when designing a safer gym, engineers and architects think: we cannot remove the equal and opposite forces, but we can reduce how strong they are by using padding that increases collision time.
Example 3: A Ball and a Bat in a Straight Line
Consider a baseball moving horizontally toward a bat. When the bat hits the ball along the same straight line, the bat exerts a large force on the ball, and the ball exerts an equal and opposite force on the bat. If the batter wants the ball to leave with a higher speed in the opposite direction, they need a larger change in the ball’s motion in a very short time, which means very large forces are involved.
Designers of bats and balls select materials that can handle these large equal and opposite forces without breaking and that give the desired performance (for example, how far the ball travels). If safety is a concern (such as with younger players), they might choose softer balls that reduce the force on both the bat and the player’s hands, while still following Newton’s Third Law.
You can safely explore Newton’s Third Law in collisions with simple setups, always making sure to follow safety rules and use only horizontal or vertical motions.
Demonstration 1: Two Rolling Cans
Place two cans on a smooth surface so they can roll. Give one can a gentle push so it rolls straight into the other. Watch what happens when they collide. Notice that both cans move after the collision. During the collision, each can pushes on the other with equal and opposite forces, but their different masses (if filled differently) can cause different changes in motion.
Demonstration 2: Egg Drop with Padding
Place an egg inside a small box with soft padding (like crumpled paper or a sponge) and drop the box vertically from a low height onto a hard floor. The floor and the box exert equal and opposite forces on each other during the collision. If the padding is good, the egg slows down over a longer time and might not break. This shows how designers use longer collision time and padding to reduce the force on fragile objects—even though the action–reaction forces between box and floor are still equal and opposite.
Newton’s Third Law tells us that whenever two objects interact, they exert forces on each other that are equal in size and opposite in direction. These forces always occur in pairs and act on different objects. In collisions along a straight line, such as cars crashing, carts bumping, or balls hitting walls, each object feels the same size force in opposite directions at the same time.
Even though the forces are equal and opposite, objects can have very different changes in motion because of their different masses. Lighter objects experience greater changes in motion for the same force, while heavier objects change motion less.
Engineers use these ideas to design solutions to collision problems. They cannot remove the action–reaction force pairs, but they can change how strong those forces are by using materials that increase the time of the collision and spread out the forces, such as crumple zones, airbags, padding, and helmets. By understanding Newton’s Third Law, mass, and motion in one dimension, we can make systems of colliding objects much safer and more effective.
