Inclined 2014

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3 (a) Explain what is meant by work done. .................................................................... .................................................................... ........... .................................................................... .................................................................... .......[1] (b) A boy on a board B slides down a slope, as shown in Fig. 3.1. Fig. 3.1 The angle of the slope to the horizontal is 30°. The total resistive force F acting on B is constant. (i) State a word equation that links the work done by the force F on B to the changes in potential and kinetic energy. .................................................................... .................................................................... ... .................................................................... ................................................................... [1] (ii) The boy on the board B moves with velocity v down the slope. The variation with time t of V is shown in Fig. 3.2.

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Transcript of Inclined 2014

Page 1: Inclined 2014

3 (a) Explain what is meant by work done.

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...............................................................................................................................................[1]

(b) A boy on a board B slides down a slope, as shown in Fig. 3.1.

Fig. 3.1

The angle of the slope to the horizontal is 30°. The total resistive force F acting on B is

constant.

(i) State a word equation that links the work done by the force F on B to the changes in

potential and kinetic energy.

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

.......................................................................................................................................[1]

(ii) The boy on the board B moves with velocity v down the slope. The variation with time t of

V is shown in Fig. 3.2.

Fig. 3.2

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The total mass of B is 75 kg. For B, from t= 0 to t= 2.5 s,

1. show that the distance moved down the slope is 9.3 m, [2]

2. calculate the gain in kinetic energy,

gain in kinetic energy = ....................................................... J [3]

3. calculate the loss in potential energy,

loss in potential energy = ....................................................... J [3]

4. calculate the resistive force F.

F= ...................................................... N [3

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4 A trolley moves down a slope, as shown in Fig. 4.1.

Fig. 4.1

The slope makes an angle of 25° with the horizontal. A constant resistive force FR acts up the slope on the trolley. At time t= 0, the trolley has velocity v= 0.50 m s−1 down the slope.

At time t = 4.0 s, v = 12 m s−1down the slope.

(a) (i) Show that the acceleration of the trolley down the slope is approximately 3 m s−2. [2]

(ii) Calculate the distance x moved by the trolley down the slope from time t= 0 to t = 4.0 s.

x = ..................................................... m [2]

(iii) On Fig. 4.2, sketch the variation with time t of distance x moved by the trolley.

Fig. 4.2[2]

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(b) The mass of the trolley is 2.0 kg.

(i) Show that the component of the weight of the trolley down the slope is 8.3 N. [1]

(ii) Calculate the resistive force FR.

FR = ...................................................... N [2

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3 (a) State Newton’s first law.

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......................................................................................................................................[1]

(b) A log of mass 450 kg is pulled up a slope by a wire attached to a motor, as shown in

Fig. 3.1.

Fig. 3.1

The angle that the slope makes with the horizontal is 12°. The frictional force acting on

the log is 650 N. The log travels with constant velocity.

(i) With reference to the motion of the log, discuss whether the log is in equilibrium.

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..............................................................................................................................[2]

(ii) Calculate the tension in the wire.

tension = ............................................. N [3]

(iii) State and explain whether the gain in the potential energy per unit time of the log is

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equal to the output power of the motor.

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2 A motor drags a log of mass 452 kg up a slope by means of a cable, as shown in Fig. 2.1.

Fig. 2.1

The slope is inclined at 14.0° to the horizontal.

(a) Show that the component of the weight of the log acting down the slope is 1070 N. [1]

(b) The log starts from rest. A constant frictional force of 525 N acts on the log. The log

accelerates up the slope at 0.130 m s–2.

(i) Calculate the tension in the cable.

tension = ............................................. N [3]9702/23/M/J/12 © UCLES 2012 [Turn over

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(ii) The log is initially at rest at point S. It is pulled through a distance of 10.0 m to

point P. Calculate, for the log,

1. the time taken to move from S to P,

time = .............................................. s [2]

2. the magnitude of the velocity at P.

velocity = ........................................ m s–1[1]

(c) The cable breaks when the log reaches point P. On Fig. 2.2, sketch the variation with

time t of the velocity v of the log. The graph should show v from the start at S until the

log returns to S. [4

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2 Two planks of wood AB and BC are inclined at an angle of 15° to the horizontal. The two

wooden planks are joined at point B, as shown in Fig. 2.1.

Fig. 2.1

A small block of metal M is released from rest at point A. It slides down the slope to B and

up the opposite side to C. Points A and C are 0.26 m above B. Assume frictional forces are

negligible.

(a) (i) Describe and explain the acceleration of M as it travels from A to B and from B to C.

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............................................................................................................................ [3]

(ii) Calculate the time taken for M to travel from A to B.

time = ............................................. s [3]

(iii) Calculate the speed of M at B.

speed = ...................................... m s–1 [2]

(b) The plank BC is adjusted so that the angle it makes with the horizontal is 30°. M is

released from rest at point A and slides down the slope to B. It then slides a distance

along the plank from B towards C.

Use the law of conservation of energy to calculate this distance. Explain your working.

distance = ............................................ m [2

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2 (a) Explain what is meant by work done.

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

..................................................................................................................................... [1]

(b) A car is travelling along a road that has a uniform downhill gradient, as shown in

Fig. 2.1.

Fig. 2.1

The car has a total mass of 850 kg. The angle of the road to the horizontal is 7.5°.

Calculate the component of the weight of the car down the slope.

component of weight = ............................................. N [2]

(c) The car in (b)is travelling at a constant speed of 25 m s–1. The driver then applies the

brakes to stop the car. The constant force resisting the motion of the car is 4600 N.

(i) Show that the deceleration of the car with the brakes applied is 4.1 m s–2 [2]

(ii) Calculate the distance the car travels from when the brakes are applied until the

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car comes to rest.

distance = ............................................. m [2]

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(iii) Calculate

1. the loss of kinetic energy of the car,

loss of kinetic energy = .............................................. J [2]

2. the work done by the resisting force of 4600 N.

work done = .............................................. J [1]

(iv) The quantities in (iii) part 1 and in (iii) part 2 are not equal. Explain why these two

quantities are not equal.

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3 (a) (i) Explain what is meant by work done.

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............................................................................................................................. [1]

(ii) Define power.

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(b) Fig. 3.1 shows part of a fairground ride with a carriage on rails.

Fig. 3.1

The carriage and passengers have a total mass of 600 kg. The carriage is travelling at a

speed of 9.5 m s–1 towards a slope inclined at 30° to the horizontal. The carriage comes

to rest after travelling up the slope to a vertical height of 4.1 m.

(i) Calculate the kinetic energy, in kJ, of the carriage and passengers as they travel

towards the slope.

kinetic energy = ............................................ kJ [3]

(ii) Show that the gain in potential energy of the carriage and passengers is 24 kJ. [2]

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(iii) Calculate the work done against the resistive force as the carriage moves up the

slope.

work done = ............................................ kJ [1]

(iv) Use your answer in (iii) to calculate the resistive force acting against the carriage

as it moves up the slope.

resistive force = ............................................. N [2

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2 A climber is supported by a rope on a vertical wall, as shown in Fig. 2.1.

Fig. 2.1

The weight W of the climber is 520 N. The rope, of negligible weight, is attached to the climber

and to a fixed point P where it makes an angle of 18° to the vertical. The reaction force R

acts at right-angles to the wall.

The climber is in equilibrium.

(a) State the conditions necessary for the climber to be in equilibrium.

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(b) Complete Fig. 2.2 by drawing a labelled vector triangle to represent the forces acting on

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the climber.

Fig. 2.2 [2]

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(c) Resolve forces or use your vector triangle to calculate

(i) the tension Tin the rope,

T= ............................................. N [2]

(ii) the reaction force R.

R= ............................................. N [1]

(d) The climber moves up the wall and the angle the rope makes with the vertical increases.

Explain why the magnitude of the tension in the rope increases.

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