Dispacement time graphs

Velocity Calculations

distance, speed, velocity, vectors and scalars

Answers to KE

Kinetic energy

1.       Calculate the kinetic energy of

 A a 1500 kg car moving at 20 m/s 300 000J (3 x 10⁵J)

B  a 3000 kg van moving at 10 m/s 150 000J (1.5 x10⁵J)

C a 10 kg shell fired at 500 m/s. 1 250 000J (1.25 x 10⁶ J)

D the 90 000 kg space shuttle landing at 100 m/s. 450 000 000J (4.5 x 10⁸J)

 

2.     You throw a ball straight up into the air.

(a) What happens to the ball’s kinetic energy as it rises? falls

(b) What is the ball’s kinetic energy at its highest point? 0

(c) What happens to the ball’s kinetic energy as it falls? increases

(d) When does the ball have maximum kinetic energy? The instant it hits the ground

 

3.     A car, a lorry and a motor bike are travelling side by side at 25m/s. Explain which has the most kinetic energy. Lorry as it has the greatest mass

 

4.     An empty lorry has a mass of 3 tonnes. It travels at a steady speed of 15m/s.

(a)   Calculate the lorry’s kinetic energy  ½ x 3000 x15² = 135 000J

(b)   What would its KE be if its mass were 6 tonnes and it still travelled at 15m/s? ½ x 3000 x15² = 270 000J (c) What will happen to the 3 tonne lorry’s kinetic energy if its speed goes up from 15 m/s to 30m/s? ½ x 3000 x30² = 1 350 000J

 

5.     A 800kg car travels at a steady 35m/s. Calculate its kinetic energy. ½  x 800 x 352 = 490 000 J

 

6.     An air rifle pellet has a mass of 10 g. It travels at 120m/s.

(i)            Write down the pellet’s mass in kilograms. 10/1000 = 0.01kg

(ii)           Calculate the pellet’s kinetic energy ½ x 0.01 x 120² = 72J

 

7.     A football has a mass of 800 g. Its speed is10m/s. Calculate its kinetic energy ½ x 0.8 x 10² = 40J

 

8.     A car has a mass of 750 kg and a velocity of 15m/s. (a)Calculate its KE. ½ x 750 x 15² = 84375 J (b) What is the work done by the brakes to stop the car 84375 J The brakes exert a maximum force of 5600 N. (c) Calculate the distance travelled before the car stops. Work = F x d, so, d = work / F = 84375/ 5600 = 15m(d) Repeat this for a speed of 30m/s KE = ½ x 750 x 30² = 337 500 J               Work = F x d, so, d = work / F = 337 500/ 5600 = 60.3m

 

 

Answers to GPE

1 The energy something has due to its high position. 1

Total 1

2 Six examples of objects with gravitational

potential energy.

One mark for each correct object. 6

One mark for object’s high position correctly identified. 6

Total 12

3 (a) Increases. 1

(b) Decreases. 1

Total 2

4 The chair, 1

because it has most mass. 1

Total 2

5 (a) Increases. 1

(b) Move the book from the floor to the middle shelf

(or from the bottom shelf to the top shelf). 1

Doing this will double its height. 1

Total 3

6 On Earth, the change in gravitational potential

energy would be greater, 1

because Earth’s gravitational field strength is greater. 1

Total 2

7 (a) (i) Weight of chair = mg = 5 × 10 = 50 N. 1

(ii) Change in E = mgh = 50 × 0.8 1

= 40 1J. 1

(b) (i) 0.400kg. 1

(ii) Change in E = mgh = 4 × 0.8 = 3.2 J. 1

Total 6

8 (a) Change in E = mgh = 0.020 × 10 x 0.70 1

= 0.14 J. 1

(b) Change in E = mgh = 0.020 × 10 x 1.60 = 0.32 J. 1

(c) Overall change = 0.32 – 0.14 = 0.18 J. 1

Total 4

Answers to worksheet

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/s

2 x 10 ⁴ 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 1.8986×10²⁷ kg 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^-23 kgm/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)