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Momentum, Work, Energy and Power Class Questions (Week 5 – Questions)
1. An object of mass m1 has a kinetic energy K1. Another object of mass m2 has a kinetic energy
K2. If the momentum of both objects is the same, the ratio 2
1
KK
is equal to
A. 1
2
mm
.
B. 2
1
mm
.
C. 1
2
mm
.
D. 2
1
mm
.(1)
2. The graph below shows the variation with displacement d of the force F applied by a spring on a cart.
5
4
3
2
1
00 1 2 3
d m / 1 0 – 2
F N/
The work done by the force in moving the cart through a distance of 2 cm is
A. 10 × 10–2J.
B. 7 × 10–2J.
C. 5 × 10–2J.
D. 2.5 × 10–2J.(1)
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3. The diagram below shows the variation with displacement x of the force F acting on an object in the direction of the displacement.
F
xxx
P
Q
R
S
TVW210
0
Which area represents the work done by the force when the displacement changes from x1 to x2?
A. QRS
B. WPRT
C. WPQV
D. VQRT(1)
4. An engine takes in an amount E of thermal energy and, as a result, does an amount W of useful work. An amount H of thermal energy is ejected. The law of conservation of energy and the efficiency of the engine are given by which of the following?
Law of conservation of energy Efficiency
A. E = W + H W
B. E = W + HEW
C. E + H = WHW
D. E + H = WHE
W–
(1)
2
5. This question is about the kinematics of an elevator (lift).
(a) Explain the difference between the gravitational mass and the inertial mass of an object.
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An elevator (lift) starts from rest on the ground floor and comes to rest at a higher floor. Its motion is controlled by an electric motor. A simplified graph of the variation of the elevator’s velocity with time is shown below.
0 .8 0
0 .7 0
0 .6 0
0 .5 0
0 .4 0
0 .3 0
0 .2 0
0 .1 0
0 .0 00 .0 1 .0 2 .0 3 .0 4 .0 5 .0 6 .0 7 .0 8 .0 9 .0 1 0 .0 11 .0 1 2 .0
tim e / s
v e lo c ity / m s – 1
(b) The mass of the elevator is 250 kg. Use this information to calculate
(i) the acceleration of the elevator during the first 0.50 s.
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(ii) the total distance travelled by the elevator.
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(iii) the minimum work required to raise the elevator to the higher floor.
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(iv) the minimum average power required to raise the elevator to the higher floor.
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(v) the efficiency of the electric motor that lifts the elevator, given that the input power to the motor is 5.0 kW.
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(c) On the graph axes below, sketch a realistic variation of velocity for the elevator. Explain your reasoning. (The simplified version is shown as a dotted line)
0 .8 0
0 .7 0
0 .6 0
0 .5 0
0 .4 0
0 .3 0
0 .2 0
0 .1 0
0 .0 00 .0 1 .0 2 .0 3 .0 4 .0 5 .0 6 .0 7 .0 8 .0 9 .0 1 0 .0 11 .0 1 2 .0
tim e / s
v e lo c ity / m s – 1
(2)
The elevator is supported by a cable. The diagram below is a free-body force diagram for when
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the elevator is moving upwards during the first 0.50 s.
te n s io n
w e ig h t
(d) In the space below, draw free-body force diagrams for the elevator during the following time intervals.
(i) 0.5 to 11.50 s (ii) 11.50 to 12.00 s
(3)
A person is standing on weighing scales in the elevator. Before the elevator rises, the reading on the scales is W.
(e) On the axes below, sketch a graph to show how the reading on the scales varies during the whole 12.00 s upward journey of the elevator. (Note that this is a sketch graph – you do not need to add any values.)
0 .0 00 .0 1 .0 2 .0 3 .0 4 .0 5 .0 6 .0 7 .0 8 .0 9 .0 1 0 .0 11 .0 1 2 .0
tim e / s
rea d in g o n sc a les
W
(3)
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(f) The elevator now returns to the ground floor where it comes to rest. Describe and explain the energy changes that take place during the whole up and down journey.
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(Total 25 marks)
6. A machine lifts an object of weight 1.5 × 103 N to a height of 10 m. The machine has an overall efficiency of 20%. The work done by the machine in raising the object is
A. 3.0 × 103 J.
B. 1.2 × 104 J.
C. 1.8 × 104 J.
D. 7.5 × 104 J.(1)
7. An electric train develops a power of 1.0 MW when travelling at a constant speed of 50 ms–1. The net resistive force acting on the train is
A. 50 MN.
B. 200 kN.
C. 20 kN.
D. 200 N.(1)
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8. This question is about the collision between two railway trucks (carts).
(a) Define linear momentum.
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In the diagram below, railway truck A is moving along a horizontal track. It collides with a stationary truck B and on collision, the two join together. Immediately before the collision, truck A is moving with speed 5.0 ms–1. Immediately after collision, the speed of the trucks is v.
BA
5 .0 m s – 1
Im m ed ia te ly b e fo re c o llis io n
Im m ed ia te ly a fte r co llis io n
BA
v
The mass of truck A is 800 kg and the mass of truck B is 1200 kg.
(b) (i) Calculate the speed v immediately after the collision.
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(ii) Calculate the total kinetic energy lost during the collision.
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(c) Suggest what has happened to the lost kinetic energy.
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(Total 8 marks)
9. The variation with time of the vertical speed of a ball falling in air is shown below.
tim e
S p eed
00 T
During the time from 0 to T, the ball gains kinetic energy and loses gravitational potential energy ΔEp. Which of the following statements is true?
A. ΔEp is equal to the gain in kinetic energy.
B. ΔEp is greater than the gain in kinetic energy.
C. ΔEp is equal to the work done against air resistance.
D. ΔEp is less than the work done against air resistance.(1)
10. The diagram below represents energy transfers in an engine.
en g in ein p u t en e rg y u sefu l o u tp u t en e rg y
w as ted en e rg y
E E
E
IN
W
O U T
The efficiency of the engine is given by the expression
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A. IN
W
EE
.
B. OUT
W
EE
.
C. IN
OUT
EE
.
D. W
OUT
EE
.(1)
11. This question is about estimating energy changes for an escalator (moving staircase).
The diagram below represents an escalator. People step on to it at point A and step off at point B.
3 0m
4 0 °A
B
(a) The escalator is 30 m long and makes an angle of 40° with the horizontal. At full capacity, 48 people step on at point A and step off at point B every minute.
(i) Calculate the potential energy gained by a person of weight 7.0 × 102 N in moving from A to B.
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(ii) Estimate the energy supplied by the escalator motor to the people every minute when the escalator is working at full capacity.
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(iii) State one assumption that you have made to obtain your answer to (ii).
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The escalator is driven by an electric motor that has an efficiency of 70%.
(b) Using your answer to (a) (ii), calculate the minimum input power required by the motor to drive the escalator.
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(Total 7 marks)
12. The point of action of a constant force F is displaced a distance d. The angle between the force and the direction of the displacement is θ, as shown below.
d
F
Which one of the following is the correct expression for the work done by the force?
A. Fd
B. Fd sin θ
C. Fd cos θ
D. Fd tan θ(1)
13. Which one of the following is a true statement about energy?
A. Energy is destroyed due to frictional forces.
B. Energy is a measure of the ability to do work.
C. More energy is available when there is a larger power.
D. Energy and power both measure the same quantity.(1)
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14. This question is about driving a metal bar into the ground.
Large metal bars can be driven into the ground using a heavy falling object.
o b jec tm ass = 2 .0 × 1 0 k g3
b arm ass = 4 0 0 k g
In the situation shown, the object has a mass 2.0 × 103 kg and the metal bar has a mass of 400 kg.
The object strikes the bar at a speed of 6.0 m s–1. It comes to rest on the bar without bouncing. As a result of the collision, the bar is driven into the ground to a depth of 0.75 m.
(a) Determine the speed of the bar immediately after the object strikes it.
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(b) Determine the average frictional force exerted by the ground on the bar.
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(Total 7 marks)
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15. A body of mass m and speed v has kinetic energy EK. A second body of mass 2m
moves at speed 2v. The kinetic energy of this second body is
A. 2KE
.
B. EK.
C. 2EK.
D. 4EK.(1)
16. A box of mass m is moved horizontally against a constant frictional force f through a distance s at constant speed v. The work done on the box is
A. 0.
B. mgs.
C. 21
mv2.
D. fs.(1)
17. A small ball P moves with speed v towards another identical ball Q along a line joining the centres of the two balls. Ball Q is at rest. Kinetic energy is conserved in the collision.
P Q a t re s t
v
Which one of the following situations is a possible outcome of the collision between the balls?
P Q
P Q
P Q
P Q
A . B .
C . D .
v v
v 3 v
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v = 0 v
v v
2 2
(1)
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18. Kinematics
(a) State the principle of conservation of energy.
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(b) An aircraft accelerates from rest along a horizontal straight runway and then takes-off. Discuss how the principle of conservation of energy applies to the energy changes that take place while the aircraft is accelerating along the runway.
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(c) The mass of the aircraft is 8.0 103 kg.
(i) The average resultant force on the aircraft while travelling along the runway is 70 kN. The speed of the aircraft just as it lifts off is 75 m s–1. Estimate the distance travelled along the runway.
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(ii) The aircraft climbs to a height of 1250 m. Calculate the potential energy gained during the climb.
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19. Mechanical power
(a) Define power.
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(b) A car is travelling with constant speed v along a horizontal straight road. There is a total resistive force F acting on the car.
Deduce that the power P to overcome the force F is
P = Fv.
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(c) A car drives up a straight incline that is 4.80 km long. The total height of the incline is 0.30 km.
4 .8 0 k m
0 .3 0 k m
The car moves up the incline at a steady speed of 16 m s−1. During the climb, the average resistive force acting on the car is 5.0 102 N. The total weight of the car and the driver is 1.2 104 N.
(i) Determine the time it takes the car to travel from the bottom to the top of the incline.
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(ii) Determine the work done against the gravitational force in travelling from the bottom to the top of the incline.
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(iii) Using your answers to (i) and (ii), calculate a value for the minimum power output of the car engine needed to move the car from the bottom to the top of the incline.
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(iv) State one reason why your answer to (iii) is only an estimate.
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(Total 11 marks)
20. This question is about energy and momentum.
A train carriage A of mass 500 kg is moving horizontally at 6.0 m s–1. It collides with another train carriage B of mass 700 kg that is initially at rest, as shown in the diagram below.
– 16 .0 m s
tra in c arriag e A5 0 0 k g
tra in carr iag e B7 0 0 k g
The graph below shows the variation with time t of the velocities of the two train carriages before, during and after the collision.
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6 .0
5 .0
4 .0
3 .0
2 .0
1 .0
0 .0
– 1 .0
– 2 .0
1 0 .09 .08 .07 .06 .05 .04 .03 .02 .01 .0
tra in carria g e B
tra in c arriag e A
t / s
v / m s – 1
(a) Use the graph to deduce that
(i) the total momentum of the system is conserved in the collision;
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(ii) the collision is elastic.
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(b) Calculate the magnitude of the average force experienced by train carriage B.
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(Total 7 marks)
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