1. 2.3 Momentum Momentum: 𝑝=𝑚𝑣 (unit: kg m s-1)
Alternative definition of N2: 𝐹=𝑚𝑎= ∆𝑝 𝑡
Impulse: change in momentum, ∆𝑝=𝐹𝑡
Area under force-time-graph gives the impulse
Momentum is ALWAYS conserved!!!

2. Ex 1: What is the momentum of a hockey puck with mass 170 g moving at 10 m s-1?

3. 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.
(041217)

4. 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 = kg, u =20 ms-1) for s. Calculate:
The impulse
The change in velocity
The final velocity

5. Collisions Total momentum before and after the collision are the same!
Inelastic collisions: (normal case)
Momentum is conserved
Formula: 𝑚 1 𝑢 1 + 𝑚 2 𝑢 2 = 𝑚 1 𝑣 1 + 𝑚 2 𝑣 2
Elastic collisions: (special case 1)
”Perfect bounce”
Momentum and kinetic energy conserved
Totally inelastic collisions: (special case 2)
”Stick together”
Formula becomes: 𝑚 1 𝑢 1 + 𝑚 2 𝑢 2 = (𝑚 1 + 𝑚 2 )𝑣
The direction is important!

6. 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

7. Example 2: A car (m = 1000 kg, v = 100 km h-1) and a truck (m = 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 = kg, 𝑢 2 = - 80 km h-1
1000 kg∙100 km h −1 −15000 kg∙80 km h −1 =(1000 kg kg)∙𝑣
𝑣= 1000 kg∙100 km h −1 −15000 kg∙80 km h − kg kg =−68.75 km h −1
Answer: The combined wreck will move at 69 km h-1 in the direction of the truck

8. Example 3: A car (m = 1000 kg, v = 100 km h-1) and a motor cycle (m = 250 kg, v = 80 km h-1) collide head on. Right after the collision the velocity of the car is 60 km h-1. What happens with the motor cycle?
Inelastic: 𝑚 1 𝑢 1 + 𝑚 2 𝑢 2 = 𝑚 1 𝑣 1 + 𝑚 2 𝑣 2
𝑚 1 =1000 kg, 𝑢 1 =100 km h-1, 𝑣 1 =60 km h-1
𝑚 2 =250 kg, 𝑢 2 = - 80 km h-1
1000 kg∙100 km h −1 −250 kg∙80 km h −1 =1000 kg∙60 km h − kg∙ v 2
𝑣= 1000 kg∙100 km h −1 −250 kg∙80 km h −1 −1000 kg∙60 km h − kg =80 km h −1
Answer: The motor cycle bounces back at 80 km h-1 in the direction of the car

9. Example 4: A Volvo (m = 2000 kg, v = 50 km h-1 from the South) and a Nissan (m = 1500 kg, v = 40 km h-1 from the West) collide at a crossroads and stick together. What happens?
Totally inelastic in 2D: 𝑚 1 𝑢 1𝑥 + 𝑚 2 𝑢 2𝑥 = (𝑚 1 + 𝑚 2 ) 𝑣 𝑥 𝑚 1 𝑢 1𝑦 + 𝑚 2 𝑢 2𝑦 = (𝑚 1 + 𝑚 2 ) 𝑣 𝑦
𝑚 1 =2000 kg, 𝑢 1𝑥 =0 km h-1, 𝑢 1𝑦 =50 km h-1
𝑚 2 =1500 kg, 𝑢 2𝑥 = 40 km h-1, 𝑢 1𝑦 =0 km h-1
X-axis: 𝑣 𝑥 = 1500 𝑘𝑔∙40 𝑘𝑚 ℎ − 𝑘𝑔+1500 𝑘𝑔 =17.14…𝑘𝑚 ℎ −1
Y-axis: 𝑣 𝑥 = 2000 𝑘𝑔∙50 𝑘𝑚 ℎ − 𝑘𝑔+1500 𝑘𝑔 =28.57…𝑘𝑚 ℎ −1
Total velocity: 𝑣= …𝑘𝑚 ℎ − …𝑘𝑚 ℎ − =33.31…𝑘𝑚 ℎ −1
Angle: 𝛼= tan − …𝑘𝑚 ℎ − …𝑘𝑚 ℎ −1 =59.0…°
Answer: The combined wreck continues at 33 km h-1 at an angle of 59° North of East