1. Forces are applied to a uniform beam pivoted at its centre. Which beam is balanced?
2. Books are placed in four bookcases as shown. Which bookcase is most likely to fall forward if pulled a little?
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3. A flat lamina is freely suspended from point P. The weight of the lamina is 2.0 N and the centre of mass is at C.
PQ = 0.40 m
QC = 0.30 m
PC = 0.50 m
The lamina is displaced to the position shown. What is the moment that will cause the lamina to swing?
A
0.60 N m clockwise
B
0.80 N m anticlockwise
C
1.0 N m clockwise
D
1.0 N m anticlockwise
4. A pivoted uniform bar is in equilibrium under the action of the forces shown.
What is the magnitude of the force F?
A 2N
B
4N
C
8N 3
D
14N
5. Two blocks are placed on a beam which balances on a pivot at its centre. The weight of the beam is negligible.
Which diagram shows the forces acting on the beam? (The length of each arrow represents the size of a force.)
6. What affects the stability of an object?
A
only its base area
B
only its base area and the location of its centre of mass
C
only its weight and its base area
D
only the location of its centre of mass
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7. A triangular piece of card with a triangular hole can be balanced on the thin edge of a ruler, as shown.
In which other position will the card balance on the ruler?
8. The stability of a bus is tested by tilting it on a ramp. The diagram shows a bus that is just about to topple over.
Where is the centre of mass of the bus? 5
9. A wooden trapdoor is hinged along one side and, when closed, is supported on the other side by a ledge.
When the trapdoor is closed, the ledge exerts an upward force of 15 N on the trapdoor. The gravitational field strength is 10 N / kg. What is the mass of the trapdoor?
A
1.5 kg
B
3.0 kg
C
30 kg
D
150 kg
10. A uniform metre rule is balanced by a 4 N weight as shown in the diagram.
What is the weight W of the metre rule?
A
1N
B
4N
C
6
16 N
D
40 N
11. Fig. 2.1 shows a device for punching holes in a piece of paper. A person applies a force F at the end of the arm. Just before the hole is made in the paper, the arm is at rest.
Fig.1.1 a) Just before the hole is made, the force upwards on the steel rod is 7.2 N. Calculate the value of F. Use the distances marked on Fig1.1.
b) The steel rod pushes the paper into the hole in the metal base with a force of 7.2 N. The end of the steel rod has an area of 2.8 × 10-5m2. Calculate the pressure exerted on the paper. State the formula that you use in your calculation.
c) The force downwards on the paper due to the rod and the force upwards on the rod due to the paper are related by Newton’s third law. State Newton’s third law. ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………
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12. Fig. 3.1 shows a crane lifting some bricks during the building of a house.
Fig.3.1
The weight of the bricks produces a turning effect, or moment, on the arm of the crane point P. The weight of the bricks is 12000 N.
about the
a) Calculate the moment of this force, using the distance marked on Fig. 3.1.
b) i.
Explain why the counterweight is necessary.
……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ii.
Suggest one advantage of being able to move the counterweight along the arm.
……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… c) Calculate the useful work done by the crane in lifting the 12000 N load through a height of 15 m. ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… 8
13. a) Fig. 4.1 shows the same vertical force of 200 N exerted by a cyclist on the pedal of a bicycle in three different positions A, B and C.
Fig.4.1 State the position, A, B or C, in which the force exerts the largest moment about the pivot. Give a reason for your answer. ……………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………
b) Fig. 2.2 shows a support for a leg in plaster and Fig. 2.3 shows a simplified diagram of the forces acting on the leg.
Fig. 4.2
Fig. 4.3
Calculate the force F needed to keep the leg in a horizontal position.
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14. Fig.6.1 shows a thin sheet of metal suspended from a hole in one corner at A. The weight of the metal is 0.10N and the centre of mass is at B. The diagram is drawn full scale.
Fig. 6.1 a) Describe in detail how you would experimentally determine the position of the centre of mass of the sheet of metal. ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… b) The sheet turns because of the moment of the weight about point A. i. Define what is meant by the moment of a force. ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ii.
Using a distance measured on Fig. 6.1, calculate the moment of the weight about point A. State clearly which distance you measured and give the unit of your final answer.
c) Fig. 6.2 and Fig. 6.3 show a thick piece of wood with one corner on a table. Fig. 6.4 shows the same piece of wood balanced on the table. B is the centre of mass.
Fig. 6.2 i.
Fig. 6.3
Fig. 6.4
Explain why in Fig. 6.2 the piece of wood falls to the right and in Fig. 6.3 it falls to the left.
……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ii.
Explain why the piece of wood in Fig. 6.4 does not fall over.
……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… iii.
Suggest how the thickness of the wood in Fig. 6.4 affects its stability.
15. Fig. 7.1 shows a wooden walking-stick that has a metal head and a rubber foot. It balances on a pencil placed 0.50 m from its rubber foot.
Fig. 7.1 a) State the distance between the centre of mass of the walking-stick and the end of the rubber foot. ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… b) The pencil is moved along the walking-stick towards its rubber foot. State and explain the motion of the walking-stick. ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… 11
16. Fig. 9.1 shows a firefighter of total weight 840 N in equilibrium at the top of a ladder that pivoted at point P.
is
Fig. 9.1 The ladder leans towards a burning building at an angle such that the centre of gravity C of the firefighter is 12 m above and 5.0 m to the right of P. The firefighter holds a hose that directs a highspeed jet of water horizontally into a burning building. a) i.
Calculate the moment M of the firefighter’s weight about P.
ii.
The jet of water causes a horizontal force R on the firefighter that acts towards the left, through C. This opposes the turning effect of his weight. Calculate the size of R that, on its own, ensures that M is exactly cancelled. ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ………………………………………………………………………………………………………………
(iii) Suggest a third force that has a turning effect about P on the ladder. ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… 12
