# Force applied at the moment of hit

I have been thinking of this problem quite long time, but couldn't find the solution: Assume that we can measure only the velocity, v, of an object with mass, m, when it hits a rigid and stationary object. How can I calculate the amount of force applied by that hitting object? The applied force would increase from zero to its maximum and then decrease to zero during the hit. So, I am asking the maximum force.

On the other hand, I wonder if my assumption, which is only v can be measured at the moment of hit, was proper.

• You might want to look up topics on the quantity called jerk. The force applied in the situation to which you refer could be modeled by something like a Dirac delta function, which you could treat as Gaussian-like for this problem I think. Sep 22, 2014 at 16:19

Forces cause a change in momentum (or a change in velocity). If you can only measure one velocity, you cannot tell how much the change is.

$$F \times \Delta t = m \times \Delta v$$ $$F =\frac{ m\times \Delta v}{\Delta t}$$

A ball that hits a floor and deforms a lot has a long interaction time. A rock that hits a solid floor has a very short interaction time. The forces are much greater for the rock because the time is short. You could not tell the difference between them by measuring only one velocity.

• What happens if the velocity remains constant for an infinitely long time? As an example, from real life, what happens if a car keeps its velocity constant long time till it hits a wall? I guess the change of momentum is not the way to go.
– Siha
Sep 20, 2014 at 21:22
• If velocity is constant, then the net force is zero. You could have an object moving in faraway space with nearly zero forces on it. Or you could have a car driving where the energy from the engine and the retarding forces of friction and drag are equal. In either case, the sum of forces is zero. Sep 20, 2014 at 21:25
• Sure, it is zero for a moving object with constant velocity. When it hits, a force will be applied to the other object. Then, we cannot talk about the zero force. In your answer, if you mean the time difference is the elapsed time from the time of hit to the time that velocity becomes zero, we still cannot calculate it correctly for the objects with different elasticities. By neglecting the heat dissipation, if two objects with quite different elasticities but same mass fall freely onto a weight scale, we read the same (almost) value of max. force...
– Siha
Sep 20, 2014 at 21:56
• "if two objects with quite different elasticities but same mass fall freely onto a weight scale, we read the same (almost) value of max. force." No. They will have the same impulse, but not the same max force. A soft ball might hit with a maximum acceleration of 3-4g. The same mass rock could have a max acceleration of >100g easily. Since the mass is the same, the maximum forces will be similarly proporition. A weight scale may not be accurate here because it will average things out. Sep 20, 2014 at 23:23