# Homework Help: Momentum change by increasing time of impact

1. Nov 15, 2005

### beginner16

hi, thank you for helping

For same momentum change if we increase the time of impact by factor ten then force is smaller by factor ten.

But why is that? I mean why doesn't a moving object at point of impact give away all of its momentum at the instant it hits something,no matter if that something is a wall or a ball or a piece of paper?

when two objects collide any combination of force and time could be used to produce certain impulse. What are the parameters that decide ( for specific impulse ) the amount of force two object colliding will exert on eachother and the amount of time collision will last?

If two balls with same mass and speed go towards eachother then momentum is zero. When they colide they both lose momentum, so how can they claim if one object loses momentum then the other object gains momentum?
I see that being true if both objects are moving in same direction or one is still. In that case one object would loose while other would gain momentum

cheers

2. Nov 15, 2005

### Astronuc

Staff Emeritus
This should help explain it.
http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html#c1, or more specifically to the question
http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html#c2

Basically a force, F, is produces a change in momentum dp/dt, and assuming that mass is constant dp/dt = m dv/dt = m a where a is acceleration, which after all is a change in velocity with respect to time.

Increasing the time over which the force is applied simply reduces the acceleration, so the time rate of change of velocity (and momentum) decreases.

The masses of the bodies involved affect the rate of transfer of momentum, as well as the stiffness of the materials. But assuming purely elastic collisions (i.e. no deformation of the mass) the mass of each object involved is main factor.

Well momentum is a vector (velocity is a vector). Depending on the coordinate system, one ball has - momentum and one has + momentum. The + momentum decreases to zero, the - momentum increases to zero. However in both cases, the magnitude of the momentum (and speed) decrease from some + value to zero.

3. Nov 15, 2005

### beginner16

So for an object to give away all of its momentum in a moment it would have to collide with an object with large mass?
It makes sense on some intuitive level, but is there way to explain why it doesn't give away all of its momentum in a brief moment if it collides with a piece of paper or something with small mass?

I'm not shure what you mean by that. Net momentum is same after collision as it was before the collision

4. Nov 15, 2005

### Astronuc

Staff Emeritus
Not quite. Assuming an elastic collision, a small mass hitting an extremely large mass will transfer very little momentum, but rather will reverse direction. The maximum transfer of momentum and kinetic energy occur when one mass hits an equal mass.

A large mass hitting a light mass keeps most of its momentum, with little or no change in direction. A light mass hitting a large mass will ricochet or recoil, retaining most of its momentum, but changing direction.

The net momentum is zero before and after, but each mass has a positive 'magnitude' of momentum, p, where p = mv, where v is the speed. Speed is always positive, but velocity, which has direction can be - or +.