Conservation Laws Momentum and Impulse

Momentum A quantity of motion resulting from an objects inertia (mass) and its velocity. The greater an objects momentum the more difficult it is to stop. Units Momentum is a vector quantity. It consists of the vector velocity. Momentum points in the same direction as the objects velocity. The sign on velocity is extremely important.

Example 1 A 5 kg mass is moving at 4 m/s. What is it’s momentum?

Impulse A change in momentum This is actually three equations in one Impulse has the same units as momentum, kg m/s This is actually three equations in one Given F and t and asked to solve for impulse Given m and v and asked to solve for impulse Problem contains F , t , m , and v

Example 2 A 5 kg mass is moving at 4 m/s speeds up to 7 m/s. What impulse caused the change in speed? There is no mention of force or time. Mass and velocity are given.

Example 3 A 6 kg mass initially at 3 m/s bounces off a wall. It losses no energy in the collision with the wall, and bounces back at 3 m/s. What impulse occurred during the bounce? Remember: Impulse is a vector, as is velocity. The +/- sign is the direction, and is very important. I set the initial motion v0 as positive. If it bounces back, then v (final) must be negative. The negative final answer means the impulse was directed opposite the initial motion There is no mention of force or time. Mass and velocity are given.

Example 4 A 4 kg mass initially at 5 m/s strikes a wall. The collision with the wall happens at an angle of 53o, as measured from the wall. No energy is lost in the collision. a. Draw an arrow in the diagram to show the path of the mass after striking the wall. b. Determine the impulse experienced by the mass. Whenever you see vectors at angles the first step in solving the problem is always components 53o 37o 53o Then we need to examine the x and y directions separately, keeping mind what the object is doing in each direction. This problem is about impulse which is a change in momentum. Did the momentum of the y-direction change during the problem? No. The vector has the same length and points in the same direction. It did not change, so there is no impulse in the y-direction. However, the x-direction did experience a change in direction, so the vector of momentum did change in the x-direction. This problem is about the x-direction only.

Example 4 A 4 kg mass initially at 5 m/s strikes a wall. The collision with the wall happens at an angle of 53o, as measured from the wall. No energy is lost in the collision. a. Draw an arrow in the diagram to show the path of the mass after striking the wall. b. Determine the impulse experienced by the mass. 53o 37o Force and time are not mentioned and the change in momentum only happens in the x-direction

Example 5 Don’t forget the initial velocity in problems like this one. Determine the final velocity for a 4.0 kg mass originally moving at 2 m/s and experiencing the forces graphed below. When it comes to graphs there are two important things worth analyzing. Which is not ringing any bells, and on top of that there are two slopes in this graph making slope unlikely Don’t forget the initial velocity in problems like this one. How about area?

Example 6 A mass experiences and impulse described by the function Determine the amount of force is applied at t = 3 s.

How Newton derived his 2nd Law Newton was working with the formula for the change in momentum and did the following: