Momentum and impulse problems

Question

1.A 1,544 kg car moving at 27.1 m/s hits a stationary truck with a mass of 3,174 kg. If the two vehicles become stuck together in the collision, how fast do they move away from the point of impact?

2.A 51 kg girl rides on a 3.2 kg skateboard. The girl on the skateboard moves at 1.1 m/s. If the girl jumps off the skateboard backwards with a velocity of 1.9 m/s, how fast does the skateboard roll away?

3.A 0.042 kg bullet moving at 472 m/s strikes a stationary 2.8 kg wooden block. The bullet passes through the block and leaves with a velocity of 253 m/s. If the block was originally at rest, how fast does it move after being hit by the bullet?

*answer and explanation please*

Answer 1

You have several problems involving the same basic principles:

Momentum is the product of mass and velocity. It has the same units as Impulse, which is commonly described as a force acting through a distance. Impulse can cause a change in momentum, and vice-versa.

When objects interact---momentum is always conserved

Consider a simple example: An object with mass M1 is moving with velocity V1. It hits another (stationary) object with mass of M2. The combined mass is now larger, so the velocity will be lower.

The momentum equation:

M1*V1 + M2*V2 = (M1+M2)*V(new)

Keep in mind that momentum is a vector quantity---meaning that the direction of motion must be taken into account. Example: 2 identical objects travelling at the same speed---one going due north, and other due east. After the collision, their combined speed will be sum of the original speed, and the direction will be northeast.

Recognize the differences between momentum and energy. While momentum is always conserved, energy is only conserved if the collision is totally elastic---meaning that all of the the energy absorbed in the collision is recovered as kinetic energy----as opposed to being converted to heat, sound, or some other form.

If all this is not "clicking" for you, spend some time with the various online resources such as Wikipedia or Khan Academy.