Monday, 1 December 2014

Momentum and Safety answers

A car has a mass of 500 kg. It is travelling at 20m/s. Calculate its momentum.

P = mv = 500 x 20 = 10 000 kgm/s

The driver applies the brakes and stops the car. What is the change in momentum? 10 000 kgm/s

The car takes 4 seconds to stop. Calculate the force exerted by the brakes.

F = ΔP/t = 10 000/4 = 2500 N

The same car is driven into a wall. It is traveling at 20 m/s. What is its momentum before it hits the wall? 10 000 kgm/s The wall stops the car. What is the change in momentum? 10 000 kgm/s The car comes to a halt in 0.006 s. Calculate the force exerted by the wall on the car.

F = ΔP/t = 10 000/0.006 = 1 666 667N

Compare this with the answer to the previous question. Very much larger

What affect does the time taken to stop have on the force applied to the car? The longer the time to stop the less the force

A human head has a mass of 4.5 kg. Calculate its momentum in a car travelling at 15m/s. P= 4.5 x 15 = 67.5 kgm/s

If the person is not wearing a seat belt and the car what happens to the speed of the head? It will hit the windscreen at 15m/s What is the speed of the head after it has hit the windscreen? 0m/s What is the change in momentum when the skull hits the car windscreen? 67.5kgm/s

The head stops in 0.002 s. calculate the force exerted on the head.

F = ΔP/t = 67.5/0.002 = 33750 N

If the car had air bags fitted the head is brought to a halt in 0.15s. Calculate the force exerted on the head now. F = ΔP/t = 67.5/0.15 = 450 N

A driver has a mass of 65kg she is not wearing a seat belt. Calculate her momentum in a car travelling at 35m/s. 65 x 35 = 2275 kgm/s

In a crash her car stops and she hits the steering wheel which stops her in 0.05s. Calculate the force exerted on her by the steering wheel. F = ΔP/t = 2275/0.05 = 45 500 N

Had she been wearing a seat belt she would have come to a halt in 0.2s.

Calculate the force exerted on her body by the seat belt. . F = ΔP/t = 2275/0.2 = 11 375 N

Thursday, 27 November 2014

Momentum

Momentum = mass x velocity kgms^-1 = kg x m/s

1. A bowling ball has a mass of 10kg and a velocity of 15m/s. Calculate its momentum. 150 kgm/s

2. A speed skater has a velocity of 15m/s and a mass of 65 kg. Calculate her momentum. 975 kgm/s

3. A bullet of mass 0.068 kg traveling horizontally at a speed of 150 m/s. Calculate its momentum. 10.2 kgm/s

4. The world record for bowling at cricket is 80 m/s. A cricket ball has a mass of 0.17kg. Calculate its momentum. 13.6 kgm/s

5. A jumbo jet has a mass of 30 000 kg. Calculate its momentum at cruising speed of 300ms^-1

9 x 10 ⁶ kgm/s

6. The Earth has a mass of 5.9742 × 10²⁴ kg. Its orbital velocity is 29.8 km/s. Calculate its momentum. 1.73 x10²⁹ kgm/s Jupiter has a mass of 1.8986×10²⁷kg and an orbital velocity of 13.06 km/s. Calculate its momentum. 2.48 x10³¹ kgm/s

7. N₂ has an atomic mass of 4.65173 x 10^-26 kg. Calculate its momentum if it has a velocity 500m/s 2.33 x 10^-23kgm/s

8. A truck of mass 2kg travels at 8 m/s towards a stationary truck of mass 6kg. After the collision they stuck together and move off in the same direction. What is their common velocity?

16kgm/s = (2+6 kg)v so 8v = 16 and v =2 m/s

9. A car of mass 2000kg, traveling at 10m/s, has a head on collision with a small sports car of mass 500kg. If both cars stop dead on colliding, what was the velocity of the sports car before the collision? Momentum after = 0 so (2000 x 10) + (500 x v) so 500v = 20000 and v = 40m/s

10. A man wearing a bullet proof vest stands on roller skates. His total mass is 80kg. A bullet of mass 20g is fired at him at a speed of 400 m/s. If the bullet is stopped by the vest and falls to the ground, what velocity will the man move at? Momentum before = (0.02kg x 400) + 0 = 8kgm/s

Momentum after = 0 + (80kg x v) = 8 kgm/s so 80v = 8 so v = 0.1m/s after being hit

How does your answer compare with “the movies”? They aren’t real. (but then you knew that)