Question

If a bike and a motorcycle are in an accident which one would experience the greater force?
Explain your answer, which law explains this? WHY?
Which will appear to have experienced the greater force?
Explain your answer, which law explains this? WHY?

Answer 1

Short answer
- The contact force on the bike and on the motorcycle during their collision is equal in magnitude and opposite in direction. (Newton’s 3rd law.)
- The bike will "appear" to be hit harder (experience the larger acceleration, greater damage, bigger change in velocity) because for the same contact force the smaller mass undergoes the larger acceleration (Newton’s 2nd law and the impulse–momentum relation).

Explanation and laws
1) Equal and opposite contact forces — Newton’s 3rd law
- When two bodies push on each other they exert forces equal in magnitude and opposite in direction at the point of contact. So at any instant the force on the bike from the motorcycle equals the force on the motorcycle from the bike.

2) Different accelerations — Newton’s 2nd law (F = ma) and impulse–momentum
- The same force acting on different masses produces different accelerations: a = F/m. The lighter object (the bike) therefore has the larger acceleration (or deceleration).
- Using impulse: J = ∫F dt = Δp. Both vehicles receive equal and opposite impulse, but Δv = Δp/m, so the smaller-mass vehicle has the larger change in velocity.

3) Why the bike appears worse off
- Larger acceleration and larger change in velocity for the bike usually means more visible damage and greater injury to the rider; thus it “appears” to have experienced the greater force.
- Also structural differences (deformation, contact time) matter: a stiffer or heavier motorcycle may transfer similar force but absorb less deformation, so the bike’s shorter stopping time and larger deceleration make the effects worse.

Note on energy
- Kinetic energy (½mv²) matters for damage: a heavier/faster motorcycle can have much more energy to dissipate in the crash, which can increase damage to the bike. But energy considerations do not change the instantaneous equality of the forces (Newton’s 3rd law).