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# Why does Force = ma rather than F = mv or F = ms? Where v equals velocity and s equals speed.?

For instance, lets say an object is moving at a constant speed of 2 m/s and hits an object at rest. According to f =ma, it wouldn’t exert any force onto the object as it has 0 acceleration. This is obviously not true, can someone explain?

### 8 Answers

- DixonLv 76 months agoFavorite Answer
Collisions are not best considered with F = ma because the momentary values of F and a during a collision are almost impossible to measure or define. Collisions are usually considered in terms of momentum (mv) and impulse (Δmv). So stick to understanding simple systems such as constant acceleration first (eg freefall) and in time you will address collisions.

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- 6 months ago
In the freshman physics lab that I use to teach, we had a cart which rolled on a horizontal track. A string attached to the cart ran over a pulley to a hanging weight. The mass of the cart and that of the hanging weight could be varied. A computer recorded the time as the cart interrupted each of four light beams at known positions and then calculated average velocities and the acceleration. We found that the acceleration was proportional to the driving force, and inversely proportional to the total mass.

In other words, F = ma describes what is observed, and that can be verified by anyone doing careful measurements.

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- Steve4PhysicsLv 76 months ago
The force and acceleration *during* a collision depend on how long the collision lasts (the contact time, t, between initial contact and the objects reaching their final velocities).

Two hard objects (e.g. steel) bouncing off each other might only have a short contact time of, say, t = 0.01s. Two softer colliding objects (e.g. rubber) will have a longer contact time, e.g. t= 0.1s.

As an example: during a collision object A (m=5kg) changes its velocity from 2m/s to -1m/s; the contact time with the other object is t=0.02s, then:

A’s velocity change Δv = (-1) – 2 = -3m/s.

A’s acceleration = Δv/t = -3/0.02 = -150 m/s²,

Force on object A = ma = 5 x (-150) = -750N

Note, the force and acceleration of object A only last for 0.02s. The other object in the collision will have force of +750N for 0.02s (though generally it will have a different velocity change and acceleration to A’s).

- Mark6 months agoReport
Thanks steve! This makes so much sense now, I would give you best answer But I dont know how to use this site yet lol

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- Andrew SmithLv 76 months ago
All definitions are made because they provide something useful.

So we DEFINED F in that way.

The definition was made because for the SAME force we can alter the acceleration by altering the mass. ie we discover that for the same force the acceleration is inversely proportional to the mass.

We can also produce experiments where we can add two, three four units of force ( eg two three four identical springs in parallel) and subsequently discover that the acceleration is also proportional to the force applied

ie we have DISCOVERED that k * F/m = a

Now all we have to do is to DEFINE the constant k as 1 ( and this ONLY applies to the SI system ) and we get F/m = a or F = ma

If you tried either of your formulae they make predictions as to what to expect if you change v.

If your predictions are found to not be true then the formula fails.

Now note that the formula does have some applicability in some conditions. Surface friction of a fluid on an object does indeed follow the path of F is proportional to v ( but not to mv )

ie if you take a flat surface and move it through a fluid keeping it so that the fluid only flows ALONG the surface you discover that the force is proportional to v.

But doubling the mass of the boat does not double this force at all.

So the formula is a failure.

You cannot simply create formulae. They must accurately represent reality for them to have any place at all.

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So to find the force you need the mass of both bodies. The speeds prior to the collision, the amount by which they compress. Then you can answer your question about forces.

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- 6 months ago
Yes, it's true that while the object is in motion there is no change in the velocity and as a result we can say there is no acceleration or deceleration. But, when it hits the object that is at rest, then it's velocity will be changed and so there will be a deceleration and at that point in time it's acceleration will no longer be zero.

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Ok, so i guess what im asking is; if an object with the mass of 5kg hits a stationary object moving at a constant speed of 2 m/s. How would you find the force exerted on the stationary object given the quantities above?

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- MorningfoxLv 76 months ago
As soon as object 1 hits object 2, there is going to be acceleration (or de-acceleration). One or both of them are going to change speed, and they're not going to do it instantly. There will be some time period (and distance) during which the speed changes, even if it's only milliseconds, or even microseconds.

(Unless we start talking about quantum physics, where F= ma doesn't apply.)

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- 6 months ago
Force is what changes the linear momentum of an object (accelerates it). There is no force acting on an object moving at a constant velocity UNTIL it hits another object. The collision slows down the moving object (force causing deceleration) and speeds up the stationary object (force causing acceleration).

You notice that it is the change of speed that relates to the force. This change of speed is also known as acceleration.

Edit: mass * velocity (aka mv) is known as momentum

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