Elastic behaviour of objects

Question

If I strike my car with a wrench with enough force to make a dent in it, then it's obvious that I won't be able to produce any acceleration in the car. But I am applying an external deforming force. Then according to Newton's third law the car body will also produce an equal and opposite force. If both forces are equal then how is a dent being made in the first case? Is there something I am missing? I have been pondering on it for quite some time.

EDIT: Is there any limit on the restoring force that a body can apply?

Answer 1

There is a misconception in your question:

it's obvious I won't be able to produce any acceleration in the car

It may be obvious to you but it isn't to me. Just because you cause a deformation does not mean that there isn't a net acceleration. Just think about a car stopped at a traffic light. A car comes up too fast from behind and hits the car in front. The bumped is bent and the car moves forward a little bit (or a lot... depending on velocities).

So even in an inelastic collision (where things deform irreversibly) you can and will transfer net momentum - there is a force $F$ applied for a time interval $\Delta t$ which results in the potential for the car to move. Of course there may be other friction in the car which results in an opposing force that stops it from moving - but there is no "law" that says there must be such a force.

In summary: inelastic impact can transfer impulse. Whether the object struck moves depends on whether there is a net force. The "equal and opposite" does not prevent a dent from happening: because there is a force from A on B, and from B on A. So the car does feel the impact, and does get dented; the wrench in return feels the force from the car.

Answer 2

If the car door was dented, then at least for a short time there was some acceleration in the door that caused it to change velocities and dent inwards. In the normal configuration where a car door is not dented, there is a limit to the normal force it can apply. When you pass this limit the forces become unbalanced and the door deforms until a new equilibrium condition is met.

You can get to equilibrium in two ways. Either the new dented configuration of the car door is able to support a greater normal force and resist further denting, or energy is dissipated during the denting process until the impact force is low enough that it reaches equilibrium with the dented car door.

In some physics problems you create an ideal surface that can respond with whatever normal forces you want without deforming. This is often a good approximation because most solids change shape very little when you apply a force. But in reality, solids do change shape when you apply a load to them. Many behave like springs when forces are small.