if an object with mass of m and velocity v hit another object, what force does it exert?
[I know this question is inappropriate and shows my lack of research, but every teacher I ask or every video I watch, says something different. Some say it's $f=m.a$ some say it's $m.v$(aka momentum), and some say it's $\frac{1}{2}.m.v^2$.even in THIS question .I'm confused]


2 Answers 2


Collision problems in physics textbooks are usually deliberately written to avoid questions of how big the forces are. Typically they invoke conservation of momentum and/or energy instead. This compares the state before the collision to the state after the collision.

If you know the forces, it is possible to figure out the accelerations and velocities at each moment, and get from the initial velocity to the final velocity. But there are difficulties during a collision.

First, objects are often assumed to be like point particles. This doesn't necessarily mean they are small. But all parts must move with the same velocity and acceleration. That is, they must be rigid. Otherwise, you can't apply the same $f=ma$ to the entire object.

Here is a video of a bat colliding with a baseball. Time Warp - baseball bat. This one is the same idea, but more fun. Explosive Bat: crushing MLB records. Ft: Smarter Every Day.

As you can see, enormous forces act over a very short time. Details of the collision get complex. It takes an expensive high speed camera to see how short the time is. That still doesn't tell you how big the forces are, and how the differ in different parts of the ball and bat.

The great thing about conservation laws is that you don't have to know. You know that, whatever happened in between, the total momentum and total energy are the same before and after. You can use that to figure out velocities after the forces settle down.


In a collision, the average impact force is given by

$$F_{ave}=m\frac{\Delta v}{\Delta t}$$

Where $\Delta v$ is the change in velocity measured over the time $\Delta t$. You need to be able to measure these changes to calculate the average force. This is essentially the answer in the link you provided.

To quote from the following link: http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html

"For collisions, the mass and change in velocity are often readily measured, but the force during the collision is not. If the time of collision can be measured, then the average force of impact can be calculated".

Hope this helps.

  • $\begingroup$ Is'nt $\frac{\Delta{v}}{\Delta{t}}=a$ ? so again it's $F=m.a$ $\endgroup$
    – MpH81679
    Commented Jan 28, 2023 at 17:47
  • 1
    $\begingroup$ Yes, but a special application of F=ma where a, and thus F, are not constant as in a collision. For a collision, the force acts for a very brief time while the colliding objects are in contact with one another. $\endgroup$
    – Bob D
    Commented Jan 28, 2023 at 17:50
  • $\begingroup$ So a is not "the acceleration right before the collision"? $\endgroup$
    – MpH81679
    Commented Jan 28, 2023 at 18:10
  • $\begingroup$ @MpH81679 a is the acceleration/deceleration of each object during the collision and due to the impact. $\endgroup$
    – Bob D
    Commented Jan 28, 2023 at 18:38

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