12.1 Momentum Momentum is a property of moving matter. Momentum describes the tendency of objects to keep going in the same direction with the same speed. Changes in momentum result from forces or create forces.

12.1 Momentum The momentum of a ball depends on its mass and velocity. Ball B has more momentum than ball A.

12.1 Calculating Momentum p = m v The momentum of a moving object is its mass multiplied by its velocity. That means momentum increases with both mass and velocity. Momentum (kg m/sec) p = m v Velocity (m/sec) Mass (kg)

Comparing momentum A car is traveling at a velocity of 13.5 m/sec (30 mph) north on a straight road. The mass of the car is 1,300 kg. A motorcycle passes the car at a speed of 30 m/sec (67 mph). The motorcycle (with rider) has a mass of 350 kg. Calculate and compare the momentum of the car and motorcycle. You are asked for momentum. You are given masses and velocities. Use: p = m v Solve for car: p = (1,300 kg) (13.5 m/s) = 17,550 kg m/s Solve for cycle: p = (350 kg) (30 m/s) = 10,500 kg m/s The car has more momentum even though it is going much slower.

12.1 Conservation of Momentum The law of conservation of momentum states when a system of interacting objects is not influenced by outside forces (like friction), the total momentum of the system cannot change. If you throw a rock forward from a skateboard, you will move backward in response.

12.1 Conservation of Momentum To see the relationship, consider two balls connected by a spring. The balls are motionless and therefore have no momentum. When you compress the spring, the third law says the balls exert equal forces (through the springs) in opposite directions on one another, -F1 = F2 Remember from Newton’s second law that the equal and opposite forces create opposite accelerations, which create opposite velocities. The accelerations are inversely proportional to the masses, so the velocities are also inversely proportional to the masses. Heavy objects end up with less velocity and light objects with more velocity. The velocities caused by the original equal and opposite forces are exactly as predicted by the law of momentum conservation.

12.1 Collisions in One Dimension A collision occurs when two or more objects hit each other. During a collision, momentum is transferred from one object to another. Collisions can be elastic or inelastic.

12.1 Collisions

Elastic collisions Two 0.165 kg billiard balls roll toward each other and collide head-on. Initially, the 10-ball has a velocity of 0.5 m/s. The 5-ball has an initial velocity of -0.7 m/s. The collision is elastic and the 5-ball rebounds with a velocity of 0.4 m/s, reversing its direction. What is the velocity of the 10-ball after the collision?

Elastic collisions You are asked for 10-ball’s velocity after collision. You are given mass, initial velocities, 5-ball’s final velocity. Diagram the motion, use m1v1 + m2v2 = m1v3 + m2v4 Solve for V3 : (0.165 kg)(0.5 m/s) + (0.165 kg) (-0.7 kg)= (0.165 kg) v3 + (0.165 kg) (0.4 m/s) V3 = -0.6 m/s

Inelastic collisions You are asked for the final velocity. A train car moving to the right at 10 m/s collides with a parked train car. They stick together and roll along the track. If the moving car has a mass of 8,000 kg and the parked car has a mass of 2,000 kg, what is their combined velocity after the collision? You are asked for the final velocity. You are given masses, and initial velocity of moving train car.

Inelastic collisions Diagram the problem, use m1v1 + m2v2 = (m1 + m2) v3 Solve for v3= (8,000 kg)(10 m/s) + (2,000 kg)(0 m/s)(8,000 + 2,000 kg) v3= 8 m/s The train cars moving together to right at 8 m/s.