Foundational Physics
Short Answer: During a collision, each object pushes on the other with an equal-magnitude, opposite-direction force, as Newton’s third law says. Their accelerations can still be different because acceleration also depends on mass. For the same interaction-force magnitude, the less massive object has the greater acceleration magnitude from that force.
Sensei’s Warning
The two equal-and-opposite collision forces act on different objects. They do not cancel when you calculate the net force on one car or one truck. Also, equal contact forces do not imply equal damage or equal injury risk.
Does a truck hit a small car harder than the car hits the truck?
It may look that way when the car is much more damaged, but the contact forces between the truck and car are equal in magnitude at every instant and point in opposite directions. The car pushes on the truck just as strongly as the truck pushes on the car.
This is Newton’s third law: the forces come as a pair, with one force acting on the car and the other on the truck.
Why does the smaller vehicle accelerate more?
Newton’s second law connects net force, mass, and acceleration. For a given force magnitude, less mass means a larger acceleration magnitude.
During the collision, the same-sized interaction forces act on the two vehicles. If we ignore other forces for this comparison, the smaller car has the larger acceleration magnitude, even though its contact force is no larger.
What would the numbers look like?
Suppose a small car has a mass of 1,000 kg and a truck has a mass of 6,000 kg. At one instant during their collision, each exerts an interaction force of magnitude 6,000 N on the other.
- Small car: 6,000 N ÷ 1,000 kg = 6 m/s2 acceleration magnitude from the contact force.
- Truck: 6,000 N ÷ 6,000 kg = 1 m/s2 acceleration magnitude from the contact force.
These accelerations point in opposite directions. The forces remain equal in magnitude, but the car’s acceleration magnitude is six times the truck’s in this example.
Why don’t the forces cancel each other?
To analyze the car, draw only forces acting on the car. The truck’s contact force belongs on the car’s free-body diagram. The car’s force on the truck belongs on the truck’s diagram instead.
Putting both forces on one diagram and canceling them would mix forces acting on different objects. That would hide the actual acceleration of each vehicle.
The takeaway
Equal collision forces do not mean equal accelerations. Newton’s third law gives equal-and-opposite interaction forces; Newton’s second law explains why objects of different masses respond differently.
When This Breaks
Newton’s third-law force pair does not stop being equal during an ordinary collision. What can fail is the simple acceleration comparison: the total net force on either vehicle may also include road friction or other external forces.
Real crashes involve rapidly varying contact forces, rotation, deformation, and safety systems. These factors matter for acceleration at different parts of a vehicle and for injury risk. The numerical example treats each vehicle as a single mass and compares the acceleration due to the mutual contact force.
Keep Exploring: Momentum and Collisions
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