P2 Revision Booklet

Energy, Work and Power

Harder (Grade B-A*)

Q1.          The picture shows players in a cricket match.

(a)     A fast bowler bowls the ball at 35 m/s. The ball has a mass of 0.16 kg.
Use the equation in the box to calculate the kinetic energy of the cricket ball as it leaves the bowler’s hand.
 
kinetic energy   =      ×   mass   ×   speed2	

Show clearly how you work out your answer.
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                     Kinetic energy = ............................................................ J
(2)

(b)     When the ball reaches the batsman it is travelling at 30 m/s. The batsman strikes the ball which moves off at 30 m/s in the opposite direction.

(i)      Use the equation in the box to calculate the change in momentum of the ball.
 
momentum    =    mass    ×    velocity	

Show clearly how you work out your answer.
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Change in momentum = ........................................................... kg m/s
(2)

(ii)     The ball is in contact with the bat for 0.001 s.
Use the equation in the box to calculate the force exerted by the bat on the ball.

Show clearly how you work out your answer.
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                                   Force = ............................................................ N
(1)

(c)     A fielder, as he catches a cricket ball, pulls his hands backwards.
Explain why this action reduces the force on his hands.
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(2)
(Total 7 marks)
 Q2.          The diagram shows a wind turbine.

(a)     The blades of the turbine are 20 metres long. On average, 15 000 kg of air, moving at a speed of 12 m/s, hit the blades every second.
Use the equation in the box to calculate the kinetic energy of the air hitting the blades every second.
 
kinetic energy   =      ×   mass   ×   speed2	

Show clearly how you work out your answer.
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                               Kinetic energy = .................................................. J
(2)

(b)     Part of the kinetic energy of the wind is transformed into electrical energy.
The diagram shows that, for the same wind speed, the power output of a turbine, in kilowatts, depends on the length of the turbine blades.

Give a reason why doubling the diameter of the blades more than doubles the power output of a turbine.
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(1)
(Total 3 marks)
 Q3.          A car is driven along a straight, snow covered, road. The graph shows how the velocity of the car changes from the moment the driver sees a very slow moving queue of traffic ahead.

(a)     Use the graph to calculate the distance the car travels while it is slowing down.
Show clearly how you work out your answer.
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Distance = ....................................... m
(3)

(b)     The car has a mass of 1200 kg.
Calculate the kinetic of the car when it travels at a speed of 12 m/s.
Write down the equation you use, and then show clearly how you work out your answer.
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Kinetic energy = ....................................... J
(2)
(Total 5 marks)
Q4.          The Boat is a theme park ride. The Boat swings backwards and forwards. The diagrams show the Boat at the top and bottom of its swing.

(a)     As the Boat swings from its position in A to its position in B, a child on the ride gains 5070 joules of kinetic energy. The child has a mass of 60 kg and is sitting at the centre.
(i)      Write down the equation which links kinetic energy, mass and speed.
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(1)

(ii)     Calculate the speed of the child as the Boat passes through B. Show clearly how you work out your final answer.
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Speed = ................................................ m/s
(2)

(b)     Sketch a graph to show how the gravitational potential energy of the child changes as the Boat swings from A to B to C. The axes have been drawn for you.

(2)
(Total 5 marks)
 Q5.          A machine is used to lift materials on a building site.

(a)     (i)      Write down the equation that links change in gravitational potential energy, change in vertical height and weight.
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(1)

(ii)     A 25 kg bag of cement is lifted from the ground to the top of the building. Calculate the gain in the gravitational potential energy of the bag of cement.
         (On Earth a 1 kg mass has a weight of 10 N.)
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Change in gravitational potential energy = ...................................... joules
(2)

(b)     The conveyor belt delivers six bags of cement each minute to the top of the building.
(i)      Calculate the useful energy transferred by the machine each second.
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Useful energy transfer each second = ................................................ J
(1)

(ii)     The machine is 40% efficient.
Use the following equation to calculate the total energy supplied to the machine each second. Show how you work out your answer.

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Total energy supplied each second = ................................................ J
(2)
(Total 6 marks)
 Q6.          The molten rock flowing from an erupting volcano can reach a speed of 8 m/s.
(i)      Write down the equation that links kinetic energy, mass and speed.
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(1)

(ii)      Calculate the kinetic energy of 1 tonne of molten rock flowing at 8 m/s. 
(1 tonne = 1000 kg)
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Kinetic energy = ............................................ joules
(1)
(Total 2 marks)

Q7.          The diagram shows an orbiter, the reusable part of a space shuttle. The data refers to a typical flight.

          (a)     (i)      What name is given to the force which keeps the orbiter in orbit around the Earth?
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(1)

(ii)     Use the following equation to calculate the kinetic energy, in joules, of the orbiter while it is in orbit.
kinetic energy = ½ mv2
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Kinetic energy = ............................. joules
(2)

(iii)     What happens to most of this kinetic energy as the orbiter re-enters the Earth’s atmosphere?
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(1)

(b)     After touchdown the orbiter decelerates uniformly coming to a halt in 50 s.
(i)      Give the equation that links acceleration, time and velocity.
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(1)

(ii)     Calculate the deceleration of the orbiter. Show clearly how you work out your answer and give the unit.
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Deceleration = ...............................
(2)

          (c)     (i)      Give the equation that links acceleration, force and mass.
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(1)

(ii)     Calculate, in newtons, the force needed to bring the orbiter to a halt. Show clearly how you work out your answer.
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Force = ............................ newtons
(1)
(Total 9 marks)
 Q8.          The diagram below shows an experiment where a pendulum swings backwards and forwards.
A pendulum is a small heavy weight suspended by a light string.

(a)     (i)      In which position, A, B or C, does the pendulum have least potential energy?
Explain your answer.
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(1)

(ii)     In which position, A, B or C, does the pendulum have greatest kinetic energy?
Explain your answer.
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(1)

(iii)     After a few minutes the size of the swings becomes smaller.
Explain why this happens.
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(1)

(b)     If the experiment were repeated on the Moon the pendulum would swing more slowly.
Suggest a reason for this.
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(2)
(Total 5 marks)
 Q9.          The diagram below shows water falling over a dam at the end of a reservoir. The water falls a vertical distance of 10 m.

(a)     Calculate the potential energy of 1 kg of water at the top of the waterfall.
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Answer ............................... J
(2)

(b)     What will be the kinetic energy of 1 kg of the water just before it lands in the pool?
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Answer ............................... J
(1)

(c)     Use your answer to (b) to calculate the speed of the water as it lands at the bottom of the waterfall.
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Answer .......................... m/s
(3)
(Total 6 marks)
 Q10.          The diagram shows a diver diving from the end of a diving board.

          The height of the diving board above the poolside is 4 m. The mass of the diver is 50 kg. Gravitational field strength is 10 N/kg.
(a)     Calculate the gain of gravitational potential energy as the diver climbs from the poolside to the diving board.
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(4)

(b)     The diver enters the water at a speed of 8 m/s.
Calculate the kinetic energy of the diver as she hits the water.
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(4)

(c)     As she hits the water her kinetic energy is different from the potential energy she gained as she climbed to the diving board. Explain why.
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(2)
(Total 10 marks)
 Energy, work and Power-Mark scheme
M1.          (a)     98
allow 1 mark for correct substitution
ie ½ × 0.16 × 35 × 35 provided no subsequent step shown
an answer of 98 000 scores 0
2

(b)     (i)      9.6
allow 1 mark for (change in velocity =) 60
ignore negative sign
2

(ii)     9600
ignore negative sign
ortheir (b)(i) ÷ 0.001 correctly calculated, unless (b) (i) equals 0
1

(c)     increases the time
1

to reduce/change momentum (to zero)
only scores if 1st mark scored
decreases rate of change of momentum scores both marks provided there are no contradictions
accept decreased acceleration/deceleration
equations on their own are insufficient
1
[7]
 M2.          (a)     1 080 000
allow 1 mark for correct substitution
ie ½ × 15 000 × 12 × 12
2

(b)     any one from:
•        KE (of wind) more than doubles
•        mass of air (hitting blades) more than doubles
•        area swept out by blades more than doubles
do not accept blades are larger / have a bigger area
•        area swept out by blades increases × 4
1
[3]
M3.          (a)     35 (m)
allow 1 mark for indicating the correct area
allow 1 mark for obtaining correct figures from the graph
allow 1 mark for calculating area of triangle (25) but
omitting the rectangle underneath (2 x 5)
3

(b)     86 400
allow 1 mark for correct substitution into the correct equation 
ie 1/2 × 1200 × 122
2
[5]
M4.          (a)     (i)      kinetic energy =  × mass × speed2
accept ke =  mv2
do not accept KE =  ms2
1

(ii)     13
allow 1 mark for correct substitution or transformation
2

(b)
if B is at the top of the curve - no marks
          PE at A maximum
PE at B minimum
PE at C just less than or = to A
do not accept wavy lines or very non-symmetrical
accept straight lines or curves
1
          difference between A and B is 5000 to 5200
1
[5]
 
M5.          (a)     (i)      gpe = weight  height
accept Ep = mgh
accept pe= mgh
1

(ii)     1200
accept values using 9.8 (1)
allow 1 mark for correct substitution
2

(b)     (i)      120
accept 
1

(ii)     300
allow b(i) ÷ 0.4 for both marks
allow 1 mark for correct transformation
2
[6]
 M6.          (i)      kinetic energy = 

accept velocity for speed
accept KE =  mv2
1

(ii)      32 000
accept 32 kJ
1
[2]
 M7.          (a)     (i)      gravity/weight
1

(ii)     2193750000000 or 2.19 × 1012
not 2.1912
allow 1 mark for the correct conversion to 7500 (m/s)
allow one mark for answer 2193750(J)
2

transferred to heat
ignore extras of sound and light
accept changed to heat
accept lost due to friction
1

(b)     (i)      acceleration = 
 
accept word speed instead of velocity
accept a = 
 
or correct rearrangement
do not accept

even if subsequent calculation correct

can gain credit if subsequent calculation correct
1

(ii)     2
ignore + or – signs
m/s2    1
accept m/s/s or ms-2
2

          (c)     (i)      force = mass × acceleration
accept correct rearrangement
accept F = m × a
do not accept

unless subsequent calculation correct
1

(ii)     156 000
accept 78 000 × their (b)(ii)(only if (b)(i) correct)
1
[9]
 M8.          (a)     (i)      B unless unqualified
for 1 mark
1

(ii)     B unless unqualified
for 1 mark
1

(iii)     energy lost, doing work against
air resistance/friction
for 1 mark
1

(b)     intensity of gravity less (not zero)
for 1 mark
          energies/restoring forces less 
for 1 mark
2
[5]
 M9.          (a)     100
gains 2 marks
          else working
gains 1 mark
2

(b)     100   ecf
for 1 mark
1

(c)     rounds to 14 (accept 14.142 or 14.14) ecf
gains 3 marks
          else working to v2 = 200
gains 2 marks
          else initial working v = 200
gains 1 mark
3
[6]
 M10.          (a)     p = mgh
= 50 × 10 × 4 = 2000
J/Nm
(see marking of calculations)
4

(b)     k = ½ mv2 
= ½ × 50 × 82 
= 1600
J/Nm
(see marking of calculations)
4

(c)     work is done against air resistance
fall of her C of G differs from rise in climbing stairs
part of gained pe used to rotate body
diver gains PE on take-off
any 2 for 1 mark each
2
[10]