Momentum Ms. Li

Momentum is a commonly used term in sports. A team that has the momentum is on the move and is going to take some effort to stop. A team that has a lot of momentum is really on the move and is going to be hard to stop.

Momentum is a physics term; it refers to the quantity of motion that an object has. A sports team that is on the move has the momentum. If an object is in motion (on the move) then it has momentum.

Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion.

The amount of momentum that an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity. In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object.massvelocity

Remember from Newton’s Second Law F =  p  t p = mv P = momentum m = mass t = time F = force

Momentum is a vector quantity. The direction of the momentum vector is the same as the direction of the velocity of the object.

Units for momentum Kg *m/s N*s

What does all this mean? The net force on an body is equal to the rate of change of momentum with a change in time.

Example A kg ball moving at 5 m/s bounces off a vertical wall without loss of speed. If the collision with the wall lasted for 0.1 s what force was exerted on the wall?

Solution The momentum of the ball changes from 0.5 Ns to -0.5 Ns in 0.1 s. The force on the ball is then (-1.0 Ns)/0.1 s The force exerted is -10 N

Example Bullets of mass 30g are being fired from a gun with a speed of 1000 m/s at a rate of 20 per second. What force is being exerted on the gun?

Solution F =  p  t If n bullets are fired:  p = n*m*v  t  t F = (20 s -1 )*(0.030 kg)*(1000m/s) F = 600 N (the units become kg*m/s 2 which is the same as a newton!)

Impulse According to newton’s second law: F =  p  t Therefore  p = F*  t Impulse = Change in momentum If the force is constant then we see can calculate the change in momentum of the object. A good example of calculating this is when a bat hits a baseball.

Now consider a collision of a tennis ball with a wall. Depending on the physical properties of the ball and wall, the speed at which the ball rebounds from the wall upon colliding with it will vary. The diagrams below depict the changes in velocity of the same ball. For each representation (vector diagram, velocity-time graph, and ticker tape pattern), indicate which case (A or B) has the greatest change in velocity, greatest acceleration, greatest momentum change, and greatest impulse.acceleration momentumimpulse

Greatest velocity change? Greatest acceleration? Greatest momentum change? Greatest Impulse?

a. The velocity change is greatest in case B. The velocity changes from +30 m/s to -28 m/s. This is a change of 58 m/s (-) and is greater than in case A (-15 m/s). b. The acceleration is greatest in case B. Acceleration depends on velocity change and the velocity change is greatest in case B (as stated above) c. The momentum change is greatest in case B. Momentum change depends on velocity change and the velocity change is greatest in case B (as stated above). d. The impulse is greatest in case B. Impulse equals momentum change and the momentum change is greatest in case B (as stated above).

Force vs time Force (N) Time (s) The area under the curve gives the total change in momentum of the body the force acts upon.

Impulse Example A force of 1000 N acts on a body of 40.0 kg initially at rest for a time interval of s. What is the velocity of the mass?

Solution The impulse is F  t = 1000N*0.05 s = 50.0 Ns This equals the amount by which the body’s momentum increases. Therefore:  v =  p/m  v =50.0 Ns/40kg=1.25 m/s