Impulse and Momentum AP Physics B

Impulse = Momentum Momentum is defined as “Inertia in Motion” Ns Consider Newton’s 2nd Law and the definition of acceleration Units of Impulse: Units of Momentum: Ns Kg x m/s Momentum is defined as “Inertia in Motion”

Example A 100 g ball is dropped from a height of h = 2.00 m above the floor. It rebounds vertically to a height of h'= 1.50 m after colliding with the floor. (a) Find the momentum of the ball immediately before it collides with the floor and immediately after it rebounds, (b) Determine the average force exerted by the floor on the ball. Assume that the time interval of the collision is 0.01 seconds.

Impulse is the Area Since J=Ft, Impulse is the AREA of a Force vs. Time graph.

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

Example A bird perched on an 8.00 cm tall swing has a mass of 52.0 g, and the base of the swing has a mass of 153 g. Assume that the swing and bird are originally at rest and that the bird takes off horizontally at 2.00 m/s. If the base can swing freely (without friction) around the pivot, how high will the base of the swing rise above its original level? How many objects do you have BEFORE the action? How many objects do you have AFTER the action? 1 2 -0.680 m/s 0.024 m

Example Granny (m=80 kg) whizzes around the rink with a velocity of 6 m/s. She suddenly collides with Ambrose (m=40 kg) who is at rest directly in her path. Rather than knock him over, she picks him up and continues in motion without "braking." Determine the velocity of Granny and Ambrose. How many objects do I have before the collision? How many objects do I have after the collision? 2 1 4 m/s

Applications of Impulse and Momentum

Air Bags Air bags are used in automobiles because they are able to minimize the effect of the force on an object involved in a collision. Air bags accomplish this by extending the time required to stop the momentum of the driver and passenger. When encountering a car collision, the driver and passenger tend to keep moving in accord with Newton's first law. Their motion carries them towards a windshield that results in a large force exerted over a short time in order to stop their momentum. If instead of hitting the windshield, the driver and passenger hit an air bag, then the time duration of the impact is increased. When hitting an object with some give such as an air bag, the time duration might be increased by a factor of 100. Increasing the time by a factor of 100 will result in a decrease in force by a factor of 100.

Boxing Fans of boxing frequently observe this same principle of minimizing the effect of a force by extending the time of collision. When a boxer recognizes that he will be hit in the head by his opponent, the boxer often relaxes his neck and allows his head to move backwards upon impact. In the boxing world, this is known as riding the punch. A boxer rides the punch in order to extend the time of impact of the glove with their head. Extending the time results in decreasing the force and thus minimizing the effect of the force in the collision. Merely increasing the collision time by a factor of ten would result in a tenfold decrease in the force.

Sports In racket and bat sports, hitters are often encouraged to follow-through when striking a ball. High-speed films of the collisions between bats/rackets and balls have shown that the act of following through serves to increase the time over which a collision occurs. This increase in time must result in a change in some other variable in the impulse-momentum change theorem. Surprisingly, the variable that is dependent upon the time in such a situation is not the force. The force in hitting is dependent upon how hard the hitter swings the bat or racket, not the time of impact. Instead, the follow-through increases the time of collision and subsequently contributes to an increase in the velocity change of the ball. By following through, a hitter can hit the ball in such a way that it leaves the bat or racket with more velocity (i.e., the ball is moving faster). In tennis, baseball, racket ball, etc., giving the ball a high velocity often leads to greater success.

Helmets Some things about the collision of an object with a helmet are outside your control. The momentum of the incoming object is a given. The amount of momentum transferred to your head and helmet is somewhat under your control, but mostly depends on things like the angle of impact that you really can't do much about. The amount of momentum transferred to the helmet is what is called "impulse". You can reduce injury if the helmet or its lining is soft enough to increase the duration of the collision, thereby reducing the force applied to the head.

Case Study

CASE STUDY

Massa crash leads to calls to re-examine F1 safety BUDAPEST, HUNGARY — Racing figures called on Formula One to re-examine safety procedures after Felipe Massa sustained life-threatening skull injuries in a high-speed accident during Hungarian Grand Prix qualifying. The 28-year-old Ferrari driver was in stable condition in the intensive care unit of a military hospital following surgery on Saturday. Massa slammed into the protective tire barriers at Hungaroring at a speed of about 120 mph after being struck in the helmet by a loose spring. The common car part had fallen out of the rear suspension of Rubens Barrichello's Brawn GP car.

Getting hit in the head by 1 kg spring at a relative velocity of about 160 mph would be fatal without a helmet even when the spring was deflected by the nose of the car and the bolster on the side of the cockpit. Even the helmet was put to the ultimate test, because the impact point was at the edge of the opening.

The helmet has to provide an artificial skull, to protect your skull The helmet has to provide an artificial skull, to protect your skull. (That means it has to be hard and strong, so it is the job of the lining to dissipate energy.) Even though the impact was right at the edge of the "eye socket", the helmet Massa was wearing did an amazing job. It appears that fragments from the helmet or visor injured his eye, although the damage could also result from a fracture as the helmet hit his head. That is the other thing the helmet has to do: absorb energy and redistribute the forces over the entire head. Massa's helmet just barely managed perform that task. He still had a fractured skull as well as a concussion from the forces that were applied to his head by the helmet.