Momentum Inertia in Motion

Definition of Momentum Momentum is the product of mass and velocity. Momentum Mass Velocity

Momentum Depends on Velocity An object must be moving in order to have momentum. Consider the truck at rest. Consider the skate boarder. He has momentum.

Momentum Depends on Mass Larger objects traveling at the same velocity as smaller objects will have greater momentum.

The Nature of Momentum Momentum is a vector quantity. –It has magnitude (how big). –It has direction (right(+) or left(-)). Direction is denoted by sign (+ or -). 235 Roll

Calculating Momentum As mentioned before, momentum is the product of mass and velocity. Given: A Sample Calculation Note: An object moving to the left would have a negative momentum.

Practice Problem 1 Calculate the momentum of the tank if its velocity is to the right.

Practice Problem 2 Calculate the momentum of the tank if its velocity is to the left.

The Law of Conservation of Momentum The Law of Conservation of Momentum states that in a closed and isolated system, the total momentum of all the objects present remains constant. This is true even for collisions. –“How is this so?” you might ask, knowing that velocities change during a collision. –The answer lies in the fact that momentum is transferred between objects (so the total can stay the same).

Collisions The collisions that we will study will involve two objects. Each object possesses its own momentum. Collisions are broken down into two categories: –Elastic (Objects Separate) –Inelastic (Objects Stick Together)

Elastic Collisions Recall, according to the Law of Conservation of Momentum that the total momentum of the system remains constant, no matter what type of collision. In an elastic collision, objects move off with separate velocities. This means that they can bounce. Or they can be projected from rest (like a cannon).

Elastic Collision Equation The elastic collision equation takes into account the momentum of each object before and after the collision. Recall, according to the law of conservation of momentum: Therefore, the equation is as follows: BeforeAfter Subscripts: I: Initial (Before) F: Final (After) Initial Momentum Object 1 Initial Momentum Object 2 Final Momentum Object 1 Final Momentum Object 2

Sample Problem (Elastic) This problem will demonstrate calculations for a bouncing collision scenario. –Two rubber balls collide and bounce, given the following information (See picture below): What is the initial momentum of the blue ball? Before 1.0kg 2.0kg v 1I = 8.0m/sv 2I = -3.0m/s What is the initial momentum of the red ball? After 1.0kg 2.0kg v 1F = -6.0m/s v 2F = ? What is the final momentum of the blue ball?What is the final momentum of the red ball?What is the final velocity of the red ball?

Practice Problem 3 (Elastic) Two air track cars collide and bounce. The red car is initially traveling at a velocity of 0.50m/s to the right while the yellow car is traveling at a velocity of 1.5m/s to the left. After the collision the red car is moving 2.0m/s to the left with the yellow car following, but not touching. Air Track 0.3kg0.8kg m red = 0.3kg m yellow = 0.8kg What is the initial momentum of the red car? What is the initial momentum of the yellow car?What is the final momentum of the red car?What is the final momentum of the yellow car?What is the final velocity of the yellow car? Collide

Sample Problem (Elastic) This problem will demonstrate the “cannon type” scenario. –The cannon and cannonball are initially at rest. –The ball then is fired at a velocity of 150m/s. m cannon = 300kg m ball = 10kg What is the initial momentum of the cannon? What is the initial momentum of the cannonball?What is the final momentum of the cannonball?What is the momentum of the cannon immediately after firing? What is the velocity of the cannon immediately after firing? Fire!

Practice Problem 4 (Elastic) A gun (m = 1.5kg), initially at rest, is fired sending its bullet (m = 0.1kg) at a velocity of. Before After What is the initial momentum of the gun and bullet? What is the total momentum of the system before firing? What is the total momentum of the system after firing? What is the final momentum of the bullet? What is the final momentum of the gun? What is the final velocity of the gun?

Inelastic Collisions Recall, according to the Law of Conservation of Momentum that the total momentum of the system remains constant, no matter what the collision. In an inelastic collision, objects stick together. This means that they have the same final velocity (v F ). N S S N v1v1 v2v2 vFvF vFvF Collide

BeforeAfter Inelastic Collision Equation The inelastic collision equation takes into account the momentum of each object before and after the collision. Here the difference lies in the fact that the objects are combined after the collision, and thus have the same final velocity (v F ). Recall, according to the law of conservation of momentum: Therefore, the equation is as follows: Initial Momentum Object 1 Initial Momentum Object 2 Final Combined Momentum Objects 1 & 2

Sample Problem (Inelastic) This problem involves a big rig hitching to its trailer. –The big rig backs up with an initial velocity of 2.0m/s and collides with the trailer, which is initially at rest. What is the initial momentum of the truck? What is the initial momentum of the trailer?What is the combined mass of the truck and trailer?What is the final velocity of the truck and trailer combo? m Truck = kg m Trailer = kg BeforeAfter Back Up

ICE Practice Problem 5 (Inelastic) Happy Penguin (m = 7.0kg) slides across the ice on a magnet with a velocity of 3.0m/s. Cool Penguin (m = 8.0kg) comes up from behind with a velocity of 5.0m/s. He, also having a magnet, will collide and stick. S N C N S H S N C N S H What is the initial momentum of Cool Penguin?What is the initial momentum of Happy Penguin?What is the combined mass of the two penguins? What is the final velocity of the penguin pair? Collide

Impulse (  p) When objects collide, their velocities change. This means that their individual momentums will also change. Impulse is simply defined the change in momentum for an individual object (denoted by  p). There are two ways to calculate impulse: –You can subtract initial momentum from final momentum. –Or you can take the product of force and time. The units for impulse are in Ns, which is equal to kgm/s

Sample Problem (Impulse) A golf ball, initially at rest, is struck by a golf club. –The golf ball (m = 0.1kg) rolls away with a velocity of 35m/s. What is the initial momentum of the ball?What is the final momentum of the ball?What is the impulse on the ball? Swing

Sample Problem Cont. (Impulse) If the ball is in contact with the club for 0.15s, what force does the ball experience? Recall,  p = -3.5kgm/s Swing

Practice Problem 6 (Impulse) A soccer ball (m = 0.4kg) approaches a player with a velocity of 13m/s (left). The player kicks the ball giving it a new velocity of 20m/s (right). What is the initial momentum of the soccer ball?What is the final momentum of the soccer ball?What is the impulse felt by the soccer ball? Kick

Sample Problem (Impulse) A baseball is struck by a bat with a force of 3000N for a duration of 0.05s. What is the change in momentum of the baseball? or Hit

Practice Problem 7 (Impulse) A tennis ball is struck with a force of 400N for a time of 0.15s. What is the impulse felt by the tennis ball? Hit

Summary All problems surrounding momentum are based on the following principles: –Momentum depends on both mass and velocity. –Momentum is conserved, regardless of collision. –Collision type determines the equation used. –Impulse is simply change in momentum. If I didn’t understand momentum, I may have been run over. There is no way my little rabbit body could have provided the impulse necessary to stop that train.