A-Level Audit: Mechanics

Instructions:
Answer as many questions as possible.
The questions become progressively more difficult.
Cancel down any fractions in your answers.
Do not put spaces in any of your answers.
Where questions involve the acceleration due
to gravity, take g to be 9.8 ms-2.
Where answers are not rational, round your
response to no more than 3 decimal places.
NOTE: Entering Fractions and Powers
In this test there are some questions where the answers contain fractions or
powers. These questions will have a special input box like the one below,
which will allow you to enter the answers.
If you have not used the special input
boxes before, you can find an explanation
about how to use them here.
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1. Is the statement below true or false?

            The forces acting on a car as it travels at a constant speed
            on a circular path around a roundabout are in equilibrium.

Write T or F in the box.

2. A person of mass 72 kg stands on a horizontal surface. Calculate the magnitude
of the normal reaction force acting on the person.
N
3. The diagram below shows two particles of mass 3 kg and 9 kg. The particle are
connected by light strings to a fixed point.

(a)    Calculate the tension in the lower string.   N

(b)    Calculate the tension in the upper string.   N

4. A block, of mass 2 kg is at rest on a rough, horizontal surface. A horizontal
force of magnitude P N acts on the block, as shown. The coefficient of
friction between the block and the surface is 0.7.

What happens to the block if   P = 15.68 N ?
        A:   It remains at rest.
        B:   It accelerates.
        C:   It moves with constant velocity.
Type the letter of your choice in this box:

5. The diagram shows a block of mass 20 kg on a rough horizontal surface. It is
attached by a light, inextensible string which passes over a smooth pulley,
to a particle of mass 3 kg. The system remains at rest.

(a)   Calculate the magnitude of the friction force acting on the block.
       N

(b)   The coefficient of friction between the block and the plane is m.
       Which of these statements is true?

A        B        C   
D        E   
Type the letter of your choice in this box:

6. A particle of mass 8 kg, is at rest on a horizontal surface with a force
of magnitude P N acting on it, in the direction shown in the diagram.

(a)   The normal reaction force on the particle has magnitude R N.
       Which of these statements is correct?

A        B        C   
D        E   

Type the letter of your choice in this box:

(b)   The friction force on the particle has magnitude F N.
       Which of these statements is correct?

A        B        C   
D        E   

Type the letter of your choice in this box:

7. The diagram shows a particle of mass 3 kg that is at rest on a rough slope,
inclined at 40 to the horizontal.

(a)  Calculate the magnitude of the normal reaction force acting on the particle.   N

(b)  Calculate the magnitude of the friction force acting on the particle.   N

8. The diagram shows a particle of mass 3 kg, which is suspended by two strings.
String 1 is horizontal and string 2 is at an angle 22 to the vertical.

(a)  Calculate the tension in string 2.  
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 N

(b)  Calculate the tension in string 1.   N

9. A velocity-time graph for a short journey along a straight line is shown below.

(a)  Calculate the distance travelled at a constant speed.   m

(b)  Calculate the total distance travelled.   m

(c)  What is the acceleration during the first 4 seconds of the journey?   ms-2

10. A stone is released from rest at a height 20 m above ground level. Assume
that as it falls it does not experience any air resistance.

(a)  Calculate the speed of the stone when it hits the ground.  
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  ms-1

(b)  Calculate the time that it takes the stone to fall to the ground.  
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 s

11. A particle moves from the point A with vector ( 3i + 4j ) metres
to the point B with position vector ( 120i - 110j ) metres in 10 seconds,
moving with constant acceleration.
The particle had velocity (i - j) ms-1 at A.

(a)  Determine the distance between the two points.   
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  m

(b)  Determine the average velocity of the particle.    ms-1

(c)  Calculate the acceleration of the particle.    ms-2

(d)  Calculate the velocity of the particle at B.    ms-1

12. Three forces, F1, F2 and F3, are in equilibrium, with
F1 = ai + bj and F2 = ci + dj

(a)  Calculate F3   
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N

(b)  Determine the magnitude of  F3   
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N

13. A man stands inside a train that is travelling at a constant speed along
a straight line. He drops a ball.

Are the statements below true or false? (Write T or F in each box.)

            A    To an observer outside the train the ball appears to move    
                   backwards and downwards.

            B    To the man, the ball appears to move backwards and    
                  downwards.

14. A lift has mass 800 kg. It is moving upwards and has an accerleration
of -0.1 ms-2. The lift is supported by a single cable.

Determine the tension in the cable.    N
15. A particle of mass 3 kg slides down a slope inclined at an angle 50 to the
horizontal. The coefficient of friction between the particle and the slope is 0.3.

Calculate the acceleration of the particle    ms-2
16. The diagram shows a shelf resting on two supports.
Are the statements below true or false? (Write T or F in each box.)

            A    There are two reaction forces acting on the shelf.   

            B    Putting a parcel on the shelf at B would increase the reaction   
                   force at A.

17. The diagrams below are intended to show the forces acting on a ladder that leans
against a smooth wall.



Which diagram is correct?   
18. A simple pendulum consists of a small mass on the end of a light string. It
swings so that the mass describes an arc of a circle.

Assume that there is no air resistance.


Which of the diagrams above shows the forces on the mass when it is

             (i)   swinging from left to right and not at the lowest position,   

            (ii)   swinging from right to left and not at the lowest position,   

            (iii)   at its lowest position.   
19. A car has mass 1500 kg and is travelling at 10 ms-1, when it hits a stationary
car of mass 1000 kg. After the collision the two cars move together.

Calculate the speed of the two cars after the collision.    ms-1
20. What is moment of the force shown about the point O?
Nm
21. What is moment of the force shown about the point O?
Nm
22. A uniform plank of mass 10 kg and length 200 cm, rests on two supports as
shown in the diagram below.
Calculate the magnitude of the reaction forces acting on the plank at A and B.

At A  
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N

At B  
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N

23. Two particles are connected by a light, inextensible string that passes over a
light smooth pulley, as shown in the diagram. The particles are released from rest.

(a)  Calculate the acceleration of the system.   
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 ms-2

(b)  Calculate the tension in the string.    N

24. The diagram shows the forces that act on a regular lamina. Determine the total
moment of these forces about the corner A.

Nm

25. The diagram shows a uniform beam that is smoothly pivoted at its centre to
a vertical wall. It is held in the position shown and is realesed
Are the statements below true or false? (Write T or F in each box.)

            A    The beam moves to a horizontal position.   

            B    The beam moves to a vertical position.   

26. Two balls, A and B, are initially at the same height above the ground. Ball A
is released so that it falls vertically from rest. Ball B is projected horizontally.
Both balls are set in motion at the same time.

Are the statements below true or false? (Write T or F in each box.)

            A    The balls hit the ground at the same time.   

            B    The balls are travelling at the same speed when they   
                   hit the ground.


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Produced by Russell Geach for CIMT - September 2006