Momentum

1. Momentum Noadswood Science, 2012

2. Momentum • To understand momentum

3. Stopping Distance • Which takes the longest time to stop – the oil tanker travelling at 25mph or the motorbike travelling at 70mph? • Why do you predict this? • What variables would you need to control to prove that mass affects the stopping time?

4. Stopping Distance • The oil tanker takes much longer to stop because it is so much more massive (it has much more mass)! • To test that mass it the cause for this difference an experiment must be set up where only the mass varies between two or more otherwise identical experiments

5. Rugby • The same science is applied to rugby – a player with much more bulk is harder to stop than a smaller player (which is where the technique becomes vital)… George Gregan and George Smith (Australia) struggle to stop Paul Sackey

6. Momentum • A moving object has momentum – this is the tendency of the object to keep moving in the same direction • It is difficult to change the direction of movement of an object with a lot of momentum Momentum (kg m/s) = Mass (kg) × Velocity (m/s) • Momentum has both a magnitude (an amount dependent on the object’s mass) and direction (dependent on the velocity of the object)

7. Momentum Questions • What is the momentum of a 5kg object travelling at 2m/s? • What is the momentum of a 40kg person running at 6m/s?

8. Momentum Questions • What is the momentum of a 5kg object travelling at 2m/s? Momentum (kg m/s) = mass (kg) x velocity (m/s) Momentum = 5 x 2 = 10kg m/s • What is the momentum of a 40kg person running at 6m/s? Momentum (kg m/s) = mass (kg) x velocity (m/s) Momentum = 40 x 6 = 240kg m/s

9. Newton’s Cradle • How does a Newton’s cradle work?

10. Conservation Of Momentum • As no external forces are acting on the objects involved, the total momentum stays the same in explosions and collisions – momentum is conserved • As momentum is conserved the mass, velocity or momentum of an object in an explosion or collision can be worked out

11. Conservation Of Momentum • Watch the demo of a vehicle colliding into another – as they collide the momentum of each object changes • One vehicle is pushed into the other, with the velocity being measured before the collision and then the velocity of both vehicles after the collision: -

12. Conservation Of Momentum • For two vehicles of the same mass – the velocity of vehicle A is halved by the impact, but the combined mass after the collision is twice he moving mass before the collision, meaning the momentum remains • For a single vehicle colliding into two vehicles the velocity of vehicle A is reduced to one third, but the combined mass after the collision is three times the initial mass, meaning the momentum remains

13. Conservation Of Momentum • If a vehicle crashes into the back of a line of cars, each car is ‘shunted’ into the car in front of it – momentum is being transferred along the line of cars to the one at the front

14. Conservation Of Momentum • Conservation of momentum: - (mass A x velocity A) + (mass B x velocity B) = 0 ∴ (mass A x velocity A) = -(mass B x velocity B)

15. Explanation • Why does a stationary boat recoil when someone jumps off it? • As someone jumps off a boat they and the boat move away with equal and opposite amounts of momentum - hence the boat moves away from them

16. Recoil • When a shell is fired from an artillery gun the gun barrel recoils backwards - this recoil is slowed by a spring, lessening the backwards momentum

17. Question 1 • A 0.5kg trolley (A) is pushed at a velocity of 1.2m/s into a stationary trolley (B) of mass 1.5kg – the two trolleys stick together after the impact • Calculate: - • The momentum of the 0.5kg trolley before the collision • The velocity of the two trolleys immediately after the impact 1.2 m/s 0 m/s A - 0.5 kg B - 1.5 kg

18. Answer 1 • The momentum of the 0.5kg trolley before the collision. Momentum = mass x velocity = 0.5 x 1.2 = 0.6kg m/s • The velocity of the two trolleys immediately after the impact Momentum = mass x velocity Momentum doesn’t change! Momentum after impact = 0.6kg m/s Mass = 1.5kg + 0.5kg = 2kg Velocity = 0.6kg ÷ 2kg = 0.3m/s

19. Question 2 • An artillery gun of mass 2000kg fires a shell of mass 20kg at a velocity of 120m/s - calculate the recoil velocity of the gun (mass gun x recoil velocity) = -(mass shell x velocity shell) (2000kg x recoil velocity) = -(20kg x 120m/s) recoil = -(20kg x 120m/s) 2000kg recoil = -1.2m/s

20. Answer 2 • A 600kg cannon recoils at a speed of 0.5m/s when a 12kg cannon ball is fired from it - calculate the velocity of the cannon ball when it leaves the cannon (mass cannon x recoil velocity) = -(mass ball x velocity ball) (600kg x 0.5m/s) = -(12kg x velocity) velocity ball = (600kg x 0.5m/s) 12kg velocity ball = 25m/s

21. Question 3 & 4 • A 30kg skater and a 40kg skater standing in the middle of an ice rink push apart - complete the following sentences using force; momentum; and velocity • They move apart with equal and opposite... • The 30kg skater move away with a bigger... than the 40kg skater • They push each other with equal and opposite... • The 30kg skater moves away at 2m/s • What is her momentum? • What is the velocity of the other skater?

22. Answer 3 • They move apart with equal and opposite momentum • The 30kg skater move away with a bigger velocity than the 40kg skater • They push each other with equal and opposite force • Momentum (kg m/s) = mass (kg) x velocity (m/s) = 30kg x 2m/s = 60kg m/s

23. Answer 4 • (mass A x velocity A) = -(mass B x velocity B) (40kg x velocity) = -(30kg x 2m/s) velocity = -(30kg x 2m/s) 40kg velocity = -1.5m/s