Question

A large truck and a car, both moving with a velocity of magnitude v, have a head-on collision. If the collision lasts for 1 s which vehicle experiences greater force of impact?
A. truck
B. car
C. both experience equal and opposite force
D. data insufficient

Answer 1

Hint: This question can be answered by using both newton’s second law and newton’s third law. According to Newton's second law for a particular system, rate of change of momentum will be equal to the external force acting on the system. According to Newton's third law for every action there will be an equal and opposite reaction.

Complete step by step answer:
First let us consider a car and truck as a single isolated system.
Now during the collision the only dominant force acting on the car is the impact force created by the truck and only dominant force acting on the truck is an impact force created by the car. Both will be in mutually opposite directions
Since we considered truck and car as a single system these two forces will become internal forces and there are no external forces(${F_{ext}} = 0$)
According to newton’s second law ${F_{ext}} = \dfrac{{d{p_{system}}}}{{dt}} = \dfrac{{d{p_{truck}}}}{{dt}} + \dfrac{{d{p_{car}}}}{{dt}} = 0$
$\eqalign{
  & \dfrac{{d{p_{truck}}}}{{dt}} = - \dfrac{{d{p_{car}}}}{{dt}} \cr
  & \left| {\dfrac{{d{p_{truck}}}}{{dt}}} \right| = \left| {\dfrac{{d{p_{car}}}}{{dt}}} \right| \cr
  & \cr} $
Where p is momentum and t is time
Negative sign indicates both act in opposite directions while magnitude of these forces are equal
Hence force on truck = -(force on car)

So, the correct answer is “Option C”.

Additional Information: According to newton’s third law if we force experienced by car due to hitting as an action then the same reaction force would be experienced by truck in an opposite direction.

Note: According to Newton’s second law external force will be zero only if we consider truck and car as a single system. If we consider truck and car as different systems then impact force acted on car due to truck will be external force for car and force acted on truck due to car will be external force for truck.