1. the Graph Shows the Variation with Time T of the Velocity V of an Object

Topic 2 test – Mechanics

Name: ______Class:______Date:______

Maximum mark = 66

1. The graph shows the variation with time t of the velocity v of an object.

Which one of the following graphs best represents the variation with time t of the acceleration a of the object?

(1)

2. A stone X is thrown vertically upwards with speed v from the top of a building. At the same time, a second stone Y is thrown vertically downwards with the same speed v as shown.

Air resistance is negligible. Which one of the following statements is true about the speeds with which the stones hit the ground at the base of the building?

A. The speed of stone X is greater than that of stone Y.

B. The speed of stone Y is greater than that of stone X.

C. The speed of stone X is equal to that of stone Y.

D. Any statement about the speeds depends on the height of the building.

(1)

3. The weight of a mass is measured on Earth using a spring balance and a lever balance, as shown below.

What change, if any, would occur in the measurements if they were repeated on the Moon’s surface?

Spring balance / Lever balance
A. / same / same
B. / same / decrease
C. / decrease / same
D. / decrease / decrease

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4. A weight is suspended from a spring. The variation with weight of the length of the spring is shown below.

What is the value of the spring constant (force constant) of the spring?

A. 0.4 N cm–1

B. 0.5 N cm–1

C. 2.0 N cm–1

D. 2.5 N cm–1

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5. When a body is accelerating, the resultant force acting on it is equal to its

A. change of momentum.

B. rate of change of momentum.

C. acceleration per unit of mass.

D. rate of change of kinetic energy.

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6. An elevator (lift) is used to either raise or lower sacks of potatoes. In the diagram, a sack of potatoes of mass 10 kg is resting on a scale that is resting on the floor of an accelerating elevator. The scale reads 12 kg.

The best estimate for the acceleration of the elevator is

A. 2.0 m s–2 downwards.

B. 2.0 m s–2 upwards.

C. 1.2 m s–2 downwards.

D. 1.2 m s–2 upwards.

(1)

7. A sphere of mass m strikes a vertical wall and bounces off it, as shown below.

The magnitude of the momentum of the sphere just before impact is pB and just after impact is pA. The sphere is in contact with the wall for time t. The magnitude of the average force exerted by the wall on the sphere is

A. .

B. .

C. .

D. . (1)

8. The velocity of a body of mass m changes by an amount Dv in a time Dt. The impulse given to the body is equal to

A. mDt.

D. mDv.

(1)

9. 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)

10. Points P and Q are at distances R and 2R respectively from the centre X of a disc, as shown below.

The disc is rotating about an axis through X, normal to the plane of the disc. Point P has linear speed v and centripetal acceleration a. Which one of the following is correct for point Q?

Linear speed / Centripetal acceleration
A. / v / a
B. / v / 2a
C. / 2v / 2a
D. / 2v / 4a

(1)

11. Linear motion

At a sports event, a skier descends a slope AB. At B there is a dip BC of width 12 m. The slope and dip are shown in the diagram below. The vertical height of the slope is 41 m.

The graph below shows the variation with time t of the speed v down the slope of the skier.

The skier, of mass 72 kg, takes 8.0 s to ski, from rest, down the length AB of the slope.

(a) Use the graph to

(i) calculate the kinetic energy EK of the skier at point B.

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(ii) determine the length of the slope.

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(b) (i) Calculate the magnitude of the change DEP in the gravitational potential energy of the skier between point A and point B.

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(ii) Use your anwers to (a)(i) and (b)(i) to determine the ratio

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(iii) Suggest what this ratio represents.

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(c) At point B of the slope, the skier leaves the ground. He “flies” across the dip and lands on the lower side at point D. The lower side C of the dip is 1.8 m below the upper side B.

(i) Calculate the time taken for an object to fall, from rest, through a vertical distance of 1.8 m. Assume negligible air resistance.

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(ii) The time calculated in (c)(i) is the time of flight of the skier across the dip. Determine the horizontal distance travelled by the skier during this time, assuming that the skier has the constant speed at which he leaves the slope at B.

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(2)

(Total 15 marks)

12. This question is about the kinematics of an elevator (lift).

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.

(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)

(2)

The elevator is supported by a cable. The diagram below is a free-body force diagram for when the elevator is moving upwards during the first 0.50 s.

(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.)

(3)

(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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(4)

(Total 25 marks)

13. This question is about momentum and the kinematics of a proposed journey to Jupiter.

(a) State the law of conservation of momentum.

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(2)

A solar propulsion engine uses solar power to ionize atoms of xenon and to accelerate them. As a result of the acceleration process, the ions are ejected from the spaceship with a speed of 3.0×104 m s–1.

(b) The mass (nucleon) number of the xenon used is 131. Deduce that the mass of one ion of xenon is 2.2 × 10–25 kg.

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(c) The original mass of the fuel is 81 kg. Deduce that, if the engine ejects 77 × 1018 xenon ions every second, the fuel will last for 1.5 years. (1 year = 3.2 × 107 s)

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(d) The mass of the spaceship is 5.4 × 102 kg. Deduce that the initial acceleration of the spaceship is 8.2 × 10–5 m s–2.

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The graph below shows the variation with time t of the acceleration a of the spaceship. The solar propulsion engine is switched on at time t = 0 when the speed of the spaceship is 1.2×103 m s–1.

(e) Explain why the acceleration of the spaceship is increasing with time.

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(f) Using data from the graph, calculate the speed of the spaceship at the time when the xenon fuel has all been used.

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(g) The distance of the spaceship from Earth when the solar propulsion engine is switched on is very small compared to the distance from Earth to Jupiter. The fuel runs out when the spaceship is a distance of 4.7 × 10–11 m from Jupiter. Estimate the total time that it would take the spaceship to travel from Earth to Jupiter.

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(2)

(Total 19 marks)