Impulse and Momentum

A measure of how difficult it is to stop a moving object Momentum A measure of how difficult it is to stop a moving object

Momentum momentum= (mass)(velocity) p = mv

Momentum If the momentum of an object is changing, as it is when a force is exerted to start or stop it, the change in momentum can be found by looking at the change in mass and velocity during the interval Change in momentum= change in [(mass)(velocity)] or Δp = Δ(mv)

Momentum Momentum is a vector. It’s direction is in the direction of the object’s velocity. The S.I. Unit for momentum is kilogram x meter /sec

Impulse The product of the force exerted on an object and the time interval during which it acts impulse = (force)(elapsed time) Or J = FΔt The S.I. Unit for impulse is (Newton)(second) Ns

Impulse/Momentum The impulse given to an object is equal to the change in momentum of the object or FΔt = mΔv The same change in momentum may be the result of a large force exerted for a short time, or a small force exerted for a long time. Impulse is the thing you do, while change in momentum is the thing you see

Example #1 Daria hits a .05kg golf ball giving it a speed of 75 m/s. What impulse does she impart to the ball?

Example # 1 Daria hits a .05kg golf ball giving it a speed of 75 m/s. What impulse does she impart to the ball? Given: m = .050kg v = 75m/s Unknown : p

Example # 2 Jessi hits a stationary .12kg hockey puck with a force that lasts for 1 x 10-2 s and makes the puck shoot across the ice with a speed of 20m/s, scoring a goal for the Hodgson Silver Eagles. With what force did Jessi hit the puck?

Example # 2 Jessi hits a stationary .12kg hockey puck with a force that lasts for 1 x 10-2 s and makes the puck shoot across the ice with a speed of 20m/s, scoring a goal for the Hodgson Silver Eagles. With what force did Jessi hit the puck? Given: Unknwn: m = .12kg F v = 20 m/s t = 1 x 10-2 Equation: F = mv =(.12kg)(20m/s) t 1 x 10-2

Example # 3 A tennis ball traveling at 10m/s is returned by Venus Williams. It leaves her racket with a speed of 36m/s in the opposite direction from which it came. A) What is the change in momentum of the tennis ball? B) If the .06kg ball is in contact with the racket for .02s, with what average force has Venus hit the ball?

Example # 3 A tennis ball traveling at 10m/s is returned by Venus Williams. It leaves her racket with a speed of 36m/s in the opposite direction from which it came. A) What is the change in momentum of the tennis ball? Given: Unknown: vo = -10m/s p vf = 36m/s m = .06kg Equ: p = m(vf - vo)

Example # 3 A tennis ball traveling at 10m/s is returned by Venus Williams. It leaves her racket with a speed of 36m/s in the opposite direction from which it came. B) If the .06kg ball is in contact with the racket for .02s, with what average force has Venus hit the ball?

Example #4 To demonstrate his new high speed camera, Santiago performs an experiment in the physics lab in which he shoots a pellet gun at a pumpkin to record the moment of impact on film. The 1.0g pellet travels at 100 m/s until it embeds itself 2.0cm into the pumpkin. What average force does the pumpkin exert to stop the pellet?

Example #4 Vavg = vf + vi = 0 + 100 = 50 m/s 2 2 2 2 Given: t= ? t= d/v = .02m / 50 m/s V = 50 m/s t= .0004 s d = .02m m= .001 kg F=(.001kg)(100m/s)/.0004 s F= 250N

Example cont’ If we did the same thing for the Y direction we would discover that the Force Net is equal to ZERO! The temptation is to treat momentum as a SCALAR...DO NOT DO THIS! SIGNS COUNT!

How about a collision? Consider 2 objects speeding toward each other. When they collide...... Due to Newton’s 3rd Law the FORCE they exert on each other are EQUAL and OPPOSITE. The TIMES of impact are also equal. Therefore, the IMPULSES of the 2 objects colliding are also EQUAL

How about a collision? If the Impulses are equal then the MOMENTUMS are also equal!

Momentum is conserved! The Law of Conservation of Momentum: “In the absence of an external force (gravity, friction), the total momentum before the collision is equal to the total momentum after the collision.”

Several Types of collisions Sometimes objects stick together or blow apart. In this case, momentum is ALWAYS conserved. When 2 objects collide and DON’T stick When 2 objects collide and stick together When 1 object breaks into 2 objects Elastic Collision = Kinetic Energy is Conserved Inelastic Collision = Kinetic Energy is NOT Conserved

Elastic Collision Since KINETIC ENERGY is conserved during the collision we call this an ELASTIC COLLISION.

Inelastic Collision Since KINETIC ENERGY was NOT conserved during the collision we call this an INELASTIC COLLISION.

Example # 6 Anthony and his twin brother Jordan have a combined mass of 200kg and are zooming along in a 100kg amusement park bumper car at 10m/s. They bump Kenya’s car, which is sitting still. Kenya has a mass of 25kg. After the elastic collision, the twins continue ahead with a speed of 4.12m/s. How fast is Kenya’s car bumped across the floor?

Example #7 Sometimes the curiosity factor at the scene of a car accident is so great that it actually produces secondary accidents as a result, while people watch to see what is going on. If an 800kg sports car slows to 13m/s to check out an accident scene and the 1200kg pick up truck behind him continues to move at 25m/s, with what velocity will the two move if they lock bumpers after a rear end collision?

Diana, a 65kg skin diver, shoots a 2kg spear with a speed of 15m/s at a fish who darts quickly away without getting hit. How fast does Diana move backwards when the spear is shot?