Momentum Momentum is a measure of how hard it is to stop or turn a moving object. What characteristics of an object would make it hard to stop or turn? Mass Velocity

Momentum p=mv p – momentum m – mass (kg) v – velocity (m/s) Momentum is a vector The units are kg m/s OR Ns

Example Calculate the momentum of a 65-kg sprinter running east at 10 m/s.

Example Calculate the momentum of a system composed of a 65-kg sprinter running east at 10 m/s and a 75-kg sprinter running north at 9.5 m/s.

Change in momentum Dp= pf – pi Dp: change in momentum pf: final momentum pi: initial momentum

Example A 0.50 kg water balloon is thrown against a wall at 32 m/s. It bursts when it hits the wall. What is its change in momentum? Now a 0.05 kg bouncy ball is thrown against a wall at 32 m/s and it bounces back with the same speed. What is its change in momentum?

Impulse (J) Impulse is the product of an external force and time, which results in a change in momentum of a particle or system. J = F t and J = p Units: N s or kg m/s (same as momentum)

Impulse formula from Newton’s 2nd law F=ma F=m Δv/t Ft=mΔv Ft = Δp This is called the impulse momentum theorem

Example A soccer player kicks a 0.45 kg ball at 25 m/s. If the goalie stops it by exerting 215 N of force, how long does it take for the ball to stop? If the goalie stops a 6.5 kg bowling ball traveling at the same velocity in the same amount of time, how much force is required?

Example Suppose a 1.5-kg brick is dropped on a glass table top from a height of 20 cm. What is the magnitude and direction of the impulse necessary to stop the brick? If the table top doesn’t shatter, and stops the brick in 0.01 s, what is the average force it exerts on the brick? What is the average force that the brick exerts on the table top during this period?

area under curve Impulse (J) on a graph F(N) t (ms) 3000 2000 1000 1 2 1 2 3 4 t (ms)

Example F(N) 2,000 1,000 0.20 0.40 0.60 0.80 t(s) This force acts on a 1.2 kg object moving at 120.0 m/s. The direction of the force is aligned with the velocity. What is the new velocity of the object?

Real-world connection Collision time affects the amount of force that an object experiences during a collision. From the impulse equation we can see that force and time are inversely proportional. That means that the longer the amount of time to bring an object to a stop in a collision, the less force is experienced.

Real-world connection (write theorem for each to explain) Air bags Wearing pads in sports Catching water balloons Bending knees when landing from jumping Follow through in sports (doesn’t change force – what else could it change in equation?) “Rebound” in collision result in large change of momentum so what do car manufacturers do to lessen chance of rebound?

Physics C Extras We just saw that the area under a force time graph is impulse, this leads to two things

Example A force acting on an object varies as a function of time according to the equation F = kt2 , where k is a constant. If the object had an initial momentum of 0 at time t = 0, what is the momentum of the object at time t=3?

Example If the momentum of an object varies with respect to time according to the function p = 3t2 – 5t + 7, find the amount of force being applied at time t=3.