qb topic 2_3 work energy power a

Topic 2-3 Work, Energy, Power

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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

K

Kis equal to

A. 1

2

m

m. B.

2

1

m

m. C.

1

2

m

m. D.

2

1

m

m.

(1)

2. A rocket is fired vertically. At its highest point, it explodes. Which one of the following describes what happens to its total momentum and total kinetic energy as a result of the explosion?

Total momentum Total kinetic energy

A. unchanged increased

B. unchanged unchanged

C. increased increased

D. increased unchanged

(1)

3. 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 / 10 –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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4. Which of the following quantities are conserved in an inelastic collision between two bodies?

Total linear momentum of the bodies Total kinetic energy of the bodies

A. yes yes

B. yes no

C. no yes

D. no no

(1)

5. 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 + H E

W

C. E + H = W H

W

D. E + H = W HE

W

–

(1)

6. Which of the following involves a change in the total energy of the objects?

A. Some ice and water as the ice melts at constant temperature.

B. An electron accelerated by a magnetic field.

C. A satellite in a circular orbit round the Earth.

D. A stone falling in a vacuum towards the Earth’s surface. (1)


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7. The diagram below represents energy transfers in an engine.

engineinput energy useful output energy

wasted energy

E E

E

IN

W

OUT

The efficiency of the engine is given by the expression

A. IN

W

E

E. B.

OUT

W

E

E. C.

IN

OUT

E

E. D.

W

OUT

E

E.

(1)

8. The variation with time of the vertical speed of a ball falling in air is shown below.

time

Speed

00 T

During the time from 0 to T, the ball gains kinetic energy and loses gravitational potential energy ∆Ep. Which of the following statements is true?

A. ∆Ep is equal to the gain in kinetic energy.

B. ∆Ep is greater than the gain in kinetic energy.

C. ∆Ep is equal to the work done against air resistance.

D. ∆Ep is less than the work done against air resistance. (1)


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9. 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)

10. 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)

11. This question is about power.

(a) Define power.

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..................................................................................................................................... (1)

(b) A constant force of magnitude F moves an object at constant speed v in the direction of the force. Deduce that the power P required to maintain constant speed is given by the expression

P = Fv

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(c) Sand falls vertically on to a horizontal conveyor belt at a rate of 60 kg s–1.

sand60 kg s

2.0 m s-1

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The conveyor belt that is driven by an engine, moves with speed 2.0 m s–1.

When the sand hits the conveyor belt, its horizontal speed is zero.

(i) Identify the force F that accelerates the sand to the speed of the conveyor belt.

........................................................................................................................... (1)

(ii) Determine the magnitude of the force F.

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........................................................................................................................... (2)

(iii) Calculate the power P required to move the conveyor belt at constant speed.

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........................................................................................................................... (1)

(iv) Determine the rate of change of kinetic energy K of the sand.

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(v) Explain why P and K are not equal.

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........................................................................................................................... (2)

(d) The engine that drives the conveyor belt has an efficiency of 40%. Calculate the input power to the engine.

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..................................................................................................................................... (2)

12. This question is about the kinematics and dynamics of circular motion.

(a) A car goes round a curve in a road at constant speed. Explain why, although its speed is constant, it is accelerating.

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..................................................................................................................................... (2)

In the diagram below, a marble (small glass sphere) rolls down a track, the bottom part of which has been bent into a loop. The end A of the track, from which the marble is released, is at a height of 0.80 m above the ground. Point B is the lowest point and point C the highest point of the loop. The diameter of the loop is 0.35 m.

A

marble

ground B

C0.80 m

0.35 m

The mass of the marble is 0.050 kg. Friction forces and any gain in kinetic energy due to the


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rotating of the marble can be ignored. The acceleration due to gravity, g = 10 ms–2.

Consider the marble when it is at point C.

(b) (i) On the diagram opposite, draw an arrow to show the direction of the resultant force acting on the marble.

(1)

(ii) State the names of the two forces acting on the marble.

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........................................................................................................................... (2)

(iii) Deduce that the speed of the marble is 3.0 ms–1.

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........................................................................................................................... (3)

(iv) Determine the resultant force acting on the marble and hence determine the reaction force of the track on the marble.

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........................................................................................................................... (4)

(Total 12 marks)


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13. 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.

objectmass = 2.0×10 kg3

barmass = 400 kg

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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..................................................................................................................................... (4)

(b) Determine the average frictional force exerted by the ground on the bar.

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..................................................................................................................................... (3)


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14. Block on an inclined plane

A block is held stationary on a frictionless inclined plane by means of a string as shown below.

string

block

inclined plane

(a) (i) On the diagram draw arrows to represent the three forces acting on the block. (3)

(ii) The angle θ of inclination of the plane is 25°. The block has mass 2.6 kg. Calculate the force in the string. You may assume that g = 9.8 m s–2.

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......................................................................................................................... (2)

(b) The string is pulled so that the block is now moving at a constant speed of 0.85 m s–1 up the inclined plane.

(i) Explain why the magnitude of the force in the string is the same as that found in (a)(ii).

.........................................................................................................................

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......................................................................................................................... (2)

(ii) Calculate the power required to move the block at this speed.

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(iii) State the rate of change of the gravitational potential energy of the block. Explain your answer.

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......................................................................................................................... (2)

15. 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.

30m

40°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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........................................................................................................................... (2)

(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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........................................................................................................................... (1)


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(iii) State one assumption that you have made to obtain your answer to (ii).

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........................................................................................................................... (1)

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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..................................................................................................................................... (3)

qb topic 2_3 work energy power a

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