Momentum
Key Concepts:
1. Determine the impulse delivered to an object based on forces, time or change in momentum.
2. Analyze the impulse delivered to an object in a situation involving collisions.
3. Analyze the momentum or impulse of an object based on force or velocity graphs.
4. Determine the velocity of an object within a system before or after a collision.
5. Setup and analyze a two-dimensional collision.
6. Differentiate amongst elastic, inelastic and perfectly inelastic collisions.
7. Determine the center of mass of a system and explain how it moves.
Key Formulas:
𝑝 = 𝑚𝑣
∆𝑝 = 𝐹∆𝑡
Clues in the Problem:
1. The problem provides a discussion of forces as well as time.
2. The setup of the problem involves any two objects hitting each other OR two objects separating from each
other.
3. The problem references a collision or explosion.
4. The problem discusses the motion of two objects in a system.
Main Process:
Conservation of Momentum
1. Determine the momentum of each object in the system before they collide or explode. This may be
numerical or symbolic.
2. Determine the total momentum of the system before they collide by adding the momentum of all objects.
3. Determine the momentum of each object in the system after they collide or explode. This may be numerical
or symbolic.
4. Determine the total momentum of the system before they collide by adding the momentum of all objects.
5. Determine whether there are external forces (those outside of the objects in the system) that are acting on
either objects and calculate the magnitude AND sign of the impulse caused by it.
6. Set the momentum of the system before the collision + impulse equal to the momentum of the system after.
Secondary Processes:
Calculating Impulse:
1. If you are given a graph of force versus time, look at the area underneath the graph.
2. If you are given velocities, calculate the change in momentum before and after the collision or explosion.
Differentiating Collision Types
1. Elastic collision – Momentum and kinetic energy are both conserved.
2. Inelastic collision – Momentum is conserved, but not kinetic energy. (Where does the energy go?)
3. Perfectly inelastic collision – Momentum is conserved, but not kinetic energy.
4. Explosion – Momentum is conserved, but not kinetic energy. Usually one velocity is negative.
The only way to distinguish between elastic and inelastic is by determine the kinetic energy!!!
Example Multiple Choice Problems:
1. A pitcher throws a ball to a catcher during the warm-up between innings. The pitcher takes 1.5 seconds to
accelerate the ball to 35 m/s during the wind-up and release of the ball. The catcher stops the ball’s motion in
0.05 seconds when the catcher catches it. Who exerts the greater impulse on the ball?
(A) The pitcher
(B) The catcher
(C) They both exert the same impulse on the ball
(D) The pitcher exerts a greater impulse, but the catcher exerts a greater change in momentum.
2.
3. What would be the speed of a 2 kg mass, originally traveling at 1 m/s, that
undergoes the motion graphed to the right?
(A) 1 m/s
(B) 2 m/s
(C) 3 m/s
(D) 4 m/s
(E) need more
information
4.
5.
6.
7.
Example Free Response:
Multiple Choice Answers:
1.
2.
3.
4.
5.
6.
7.
C
B
D
B
ACD
D
C