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Force and acceleration

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deepsender    100
Can a physics wizard please break down the formula: Force = Mass * Acceleration. My application is one in which one object strikes another object, and I want to know the amount of force that is transferred from one object to another. 1. Is acceleration simply the object's velocity squared, or is it a velocity that is changing? 2. If the velocity of an object is increasing at the time it strikes another object, does any acceleration get transferred to the second object? 3. If an object's velocity is decreasing when it strikes another object, does it transfer less force than if it were at a steady velocity?

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TheAdmiral    1122
Hi deepsender.

1. Acceleration is the rate of change of velocity with respect to time. On a continuous level, it's represented as the derivative dv/dt or d²x/dt² (Acceleration is to velocity as velocity is to position). In a discrete system, the instantaneous acceleration is the change in velocity since the last measure, over the time elapsed since that measure.

2. This depends on the elasticity of the collision. If the collision is instantaneous (and the objects bounce off each other immediately), the acceleration makes no difference, only the momenta (and hence velocities) at the impact point. If the objects clump together or compress upon collision, the accelerating object will pass some of its force onto the other object for as long as they are in contact.

3. This is the same as 2, except that the acceleration is now negative.

If you're looking to calculate the velocities of two accelerating (rigid) bodies after a collision, you're best off avoiding Newton's second law, and trading it in for a more appropriate model. You may want to look into coefficients of restitution.
Unless your colliding bodies are soft or compressible, ignore acceleration and calculate the momenta of the objects at the moment of impact. Apply conservation of momentum and divide the total up according to your restitution constants.
If they are compressible, use E = Fs (Kinetic Energy = Force x Distance) where s is the distance taken to bring the bodies to equilibrium.


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JohnBolton    1372
In an "elastic" collision (where the colliding objects don't change shape and energy is not lost), the collision is instantaneous, and force and acceleration are not involved at all.

The result of the collision is determined by two principles -- conservation of momentum (the total momentum doesn't change) and conservation of energy (the total energy doesn't change).

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