A couple of demos • Same mass • Different masses • Opposite directions
Linear momentum p = mv (kg·m/s)
Some notes on linear momentum • Momentum is a vector in the same direction as the velocity of the object • For an isolated system (no external forces) momentum is conserved. That is, po = p • If the problem describes a collision or “explosion”, it almost always indicates you will use conservation of momentum • If no external forces act on a system, velocity of the center of mass is constant
More on this “velocity of center of mass is constant” thing
Ex. Two carts of equal mass are on a frictionless track. Cart A moves with a speed of +1.0 m/s and Cart B is at rest. Cart A collides with Cart B, and comes to rest. What is the velocity of Cart B after the collision?
Ex. Cart A (0.40 kg) is moving with a velocity of +1.0 m/s. It collides with cart B (0.20 kg) which is stationary. After the collision, Cart A moves with a velocity of +0.40 m/s. What is the velocity of Cart B after the collision?
Ex. Cart A (0.40 kg) moves with a velocity of +1.0 m/s. Cart B (0.20 kg) moves with a speed of −1.0 m/s. The two carts collide and stick together. What is the final velocity of the two carts after the collision?
Ex. Two students on roller blades, Larry (50 kg) and Curly (75 kg) are at rest. They push away from each other and move in opposite directions. For a given time interval after the push, Larry travels 3.0 m. How far does Curly travel during the same time interval?
The raft problem
Elastic and Inelastic Collisions • Elastic collision – one in which kinetic energy is conserved (Ko = K) • Inelastic Collision – one in which kinetic energy is not conserved (Ko ≠ K) A completely inelastic collision is one in which two objects stick together after a collision. • If no external forces act on the system, momentum is conserved in both types of collisions.
Impulse – Behold! I bring thee a derivation!
Impulse-Momentum Theorem J = FavΔt = Δp (N·s) or kg·m/s
A couple of notes • Impulse-momentum is really just another way to write Newton’s Second Law • The momentum of an object only changes if there is a net external force exerted on the object • Impulse is a vector in the direction of the net force exerted on the object • Both force and time affect the change in momentum. A small force exerted for a short time period can change the momentum the same as a large force exerted of a short period of time
Examples of impulse • Follow through (tennis, punting, swing a bat, bunting) • The Fosbury Flop • Air bags • Jumping from a table with knees locked/bent • Boxing • The egg and the sheet
Force vs time graphs
Ex. A 60 kg person is traveling in a car that is moving at 16 m/s when the car hits a barrier. The person is not wearing a seat belt but is stopped by an air bag in a time interval of 0.20 s. What is the average force the air bag exerts on the person while stopping him?
Generalized impulse-momentum principle po + FavΔt = p
Impulse-momentum bar charts • Collision of objects of different momenta moving in opposite directions (no external forces) • Collision of one car with a wall 1) System is car only 2) Wall exerts an external force) • Thud ball and springy ball 1) system is the ball 2) Floor exerts an external force). • Rocket propulsion: 1) fuel and rocket are the system 2) rocket alone is the system
Ex. A 0.020 kg bullet traveling horizontally at a speed of 250 m/s embeds in a 1.0 kg block of wood resting on a table. Determine the speed of the bullet and wood block together immediately after the bullet embeds in the block. Is the collision elastic or inelastic? Justify your answer numerically.
Ex. The record for the highest stunt fall without a parachute is 71 m. The 80 kg stuntman’s fall was stopped by a large air cushion, into which he sank about 4.0 m. His speed was about 36 m/s when he reached the top of the air cushion. Estimate the average force the cushion exerts on the stuntman while stopping him.
Collisions in two dimensions
v vo
vo
If the two cars have initial velocities as shown above, and collide and stick together at the origin, explain why the resulting momentum of their combine masses will be in the direction shown. Your explanation should use the components of momentum for each car.
v
45° 45°
A circular disk is at the origin as shown above. It explodes into three pieces. The largest piece moves along the –x-axis. The other two pieces, each with half the mass of the largest, move at 45° above and the +x-axis. What is the speed of each of the smaller pieces in terms of the speed of the larger piece v?
