Question

How do you calculate the change in momentum of an object?

Answer 1

There are two possible ways depending on the problem.

1) The change in momentum of an object is its mass times the change in its velocity. `\Delta p=m*(\Deltav)=m*(v_f-v_i)`.

`v_f` and `v_i` are the final and initial velocities. Remember to use the right signs when substituting `v_f` and `v_i`

Example) A 3kg mass initially moving 4m/s to the right rebounds off of a wall and begins travelling to the left at 2m/s.

Taking "right" to be the positive direction: `v_i`=+4m/s, `v_f`= –2m/s, and m=3kg. Substituting,
`\Delta p=3kg*(-2`m/s`-4`m/s)`=-18` kg m/s

2) The change in the momentum of an object can also be found by considering the force acting on it. If a force, `F`, acts on an object for a time, `\Delta t`, the change in the objects momentum is `\Delta p= F*\Delta t`.
Remember to use the right sign when substituting `F`. For example, a force to the left could be negative.

Lastly, if your object is moving both horizontally and vertically then `\Delta p` has a vertical and horizontal component. If this is the case, the above equations still work for each component separately, Ex) To find the horizontal component of `\Delta p` use the horizontal component of `v_i, v_f` or `F` in the above equations.