Momentum and impulse problems

Question

1.A 6,900 kg freight truck accelerates from 5 m/s to 48 m/s in 12 s by applying a constant force. What change in momentum occurs?

2.A 6,900 kg freight truck accelerates from 10 m/s to 41 m/s in 5.7 s by applying a constant force. How much force was applied to the truck?

3.A metal sphere with a mass of 0.044 kg rolls along a friction-less surface at 2.8 m/s and strikes a stationary sphere having a mass of 0.039 kg. The first sphere stops completely.  The spheres are in contact for 0.006 s before the second sphere is shot off down the track. What is the force applied to the second ball?

4.

An 4.1 kg bowling ball rolls with a velocity of 1.9 m/s and strikes a stationary 1.8 kg bowling ball. The first ball stops after the collision. How fast does the second bowling ball roll away after the collision?

*answer and explanation*

Answer 1

Answer 2

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.

Add to the above: Us F =ma for the questions relating to the effect of an applied force.

And velocity = acceleration* time (v = a*t)