7. Momentum and impulse Momentum: 𝑝=𝑚𝑣 (unit: kg m s-1) Change in momentum (∆𝑝) is called impulse (𝐼): ∆𝑝=𝐼=𝐹𝑡 Momentum is ALWAYS conserved!
Ex 1: What is the momentum of a hockey puck with mass 170 g moving at 10 m s-1?
Ex 2: Which action requires more force, to block the puck (m = 0,17 kg, u = 10 m s-1) or to catch it? Both actions take 0.10 s. https://im.mtv.fi/image/4508284/landscape16_9/1024/576/6b96fc3dd44ef2b34d3cb0cbd63bd9c2/ea/atte-engren-venaja-ottelussa.jpg (041217)
Ex. 3: A force of 100 N from a racket acts on a tennis ball (m = 0 Ex. 3: A force of 100 N from a racket acts on a tennis ball (m = 0.090 kg, u =20 ms-1) for 0.045 s. Calculate: The impulse The change in velocity The final velocity
8. Collisions Total momentum before and after the collision are the same! Inelastic collisions: Momentum is conserved Formula: 𝑚 1 𝑢 1 + 𝑚 2 𝑢 2 = 𝑚 1 𝑣 1 + 𝑚 2 𝑣 2 Elastic collisions: ”Perfect bounce” Momentum and kinetic energy conserved Totally inelastic collisions: ”Stick together” Formula becomes: 𝑚 1 𝑢 1 + 𝑚 2 𝑢 2 = (𝑚 1 + 𝑚 2 )𝑣 The direction is important!
Example 1: An ice skater (m = 49 kg) at rest catches a ball (m = 1 kg) with velocity 10 m s-1. What happens? Totally inelastic: 𝑚 1 𝑢 1 + 𝑚 2 𝑢 2 = (𝑚 1 + 𝑚 2 )𝑣 𝑚 1 =49 kg, 𝑢 1 =0 m s-1 𝑚 2 =1 kg, 𝑢 2 =10 m s-1 49 kg∙0 m s −1 +1 kg∙10 m s −1 =(49 kg+1 kg)∙𝑣 𝑣= 1 kg∙10 m s −1 49 kg+1 kg =0.2 m s −1 Answer: the skater (holding the ball) will start moving with 0.2 m s-1 in the same direction as the ball that hit her
Example 2: A car (m = 1000 kg, v = 100 km h-1) and a truck (m = 15 000 kg, v = 80 km h-1) collide head on and stick together. What happens? Totally inelastic: 𝑚 1 𝑢 1 + 𝑚 2 𝑢 2 = (𝑚 1 + 𝑚 2 )𝑣 𝑚 1 =1000 kg, 𝑢 1 =100 km h-1 𝑚 2 =15 000 kg, 𝑢 2 = - 80 km h-1 1000 kg∙100 km h −1 −15000 kg∙80 km h −1 =(1000 kg+15000 kg)∙𝑣 𝑣= 1000 kg∙100 km h −1 −15000 kg∙80 km h −1 1000 kg+15000 kg =−68.75 km h −1 Answer: The combined wreck will move at 69 km h-1 in the direction of the truck
P. 23: 7.1, 7.2, 7.3, 7.4, 7.5, (extra 7.7) P. 27-: 8.1 (b) means the first puck stops 8.2 8.3 8.4 the energy from the push is converted to kinetic energy shared between them 8.5 (extra 8.9)