Momentum CHAPTER # 5 Momentum

So What’s Momentum ? Momentum (p) = mass (m) x velocity (v) p= mv So, A really slow moving truck and an extremely fast roller skate can have the same momentum.

p =mv p=mv 1 kg (10 m/s) = 10 kg x m/s 1000 kg (.01 m/s) = 10 kg x m/s 10 m/sec 1 kg .01 m/sec 1000 kg

Question : What is the momentum of an 80kg runner moving at a speed of 2.5 m/s?

Impulse and Momentum Ft = mv If momentum changes, it’s because mass or velocity change. Most often mass doesn’t change so velocity changes and that is acceleration. And mass x acceleration = force Applying a force over a time interval to an object changes the momentum Force x time interval = Impulse Impulse = F t or Ft = mv Ft = mv

MOMENTUM To INCREASE MOMENTUM, apply the greatest force possible for as long as possible. Examples : pulling a sling shot drawing an arrow in a bow all the way back hitting a golfball FORCE TIME

MOMENTUM Ft Decreasing Momentum Which would it be more safe to hit in a car ? Knowing the physics helps us understand why hitting a soft object is better than hitting a hard one. Ft mv Ft mv

MOMENTUM In each case, the momentum is decreased by the same amount or impulse (force x time) Hitting the haystack extends the impact time The longer impact time reduces the force of impact and decreases the deceleration.

EXAMPLES OF DECREASING MOMENTUM Bruiser Bruno on boxing … Increased impact time reduces force of impact Barney Jervais on bungee Jumping … Ft = change in momentum Ft = change in momentum POOF ! CRUNCH ! Ft = Δmv applies here. mv = the momentum gained before the cord begins to stretch that we wish to change. Ft = the impulse the cord supplies to reduce the momentum to zero. Because the rubber cord stretches for a long time the average force on the jumper is small.

Decrease Momentum over short time, increase force Karate experts sever bricks

Questions : When a dish falls, will the impulse be less if it lands on a carpet than if it lands on a hard ceramic tile floor ? The impulse would be the same for either surface because there is the same momentum change for each. It is the force that is less for the impulse on the carpet because of the greater time of momentum change. There is a difference between impulse and impact. If a boxer is able to increase the impact time by 5 times by “riding” with a punch, by how much will the force of impact be reduced? Since the time of impact increases by 5 times, the force of impact will be reduced by 5 times.

The Law of Conservation of Momentum In the absence of an external force, the momentum of a system remains unchanged. This means that, when all of the forces are internal (for EXAMPLE: the nucleus of an atom undergoing radioactive decay, cars colliding, or stars exploding; the net momentum of the system before and after the event is the same.

QUESTIONS 1. Newton’s second law states that if no net force is exerted on a system, no acceleration occurs. Does it follow that no change in momentum occurs? No acceleration means that no change occurs in velocity of momentum. 2. Newton’s 3rd law states that the forces exerted on a cannon and cannonball are equal and opposite. Does it follow that the impulse exerted on the cannon and cannonball are also equal and opposite? Since the time interval and forces are equal and opposite, the impulses (F x t) are also equal and opposite.

COLLISIONS ELASTIC COLLISIONS INELASTIC COLLISIONS Momentum transfer from one Object to another . Is a Newton’s cradle like the one Pictured here, an example of an elastic or inelastic collision?

Problem Solving #1 A 6 kg fish swimming at 1 m/sec swallows a 2 kg fish that is at rest. Find the velocity of the fish immediately after “lunch”. net momentum before = net momentum after (net mv)before = (net mv)after (6 kg)(1 m/sec) + (2 kg)(0 m/sec) = (6 kg + 2 kg)(vafter) 6 kg.m/sec = (8 kg)(vafter) vafter = 6 kg.m/sec / 8 kg 8 kg vafter = ¾ m/sec vafter =