P.3.4.1.2 Moments

A bird sits on a uniform rod suspended from vertical wires P and Q.

The rod has a weight W and is 15.0 cm long. The weight of the bird is 2W and acts at a distance x from P.

What is the value of x when the tension in P is half the tension in Q?

• 7.50 cm

• 10.0 cm

• 11.3 cm

• 15.0 cm

A non-uniform sign is 0.80 m long and has a weight of 18 N. It is suspended from two vertical springs P and Q. The springs obey Hooke’s law and the spring constant of each spring is 240 N m^–1

The top end of spring P is fixed and the top end of spring Q is adjusted until the sign is horizontal and in equilibrium. What is the extension of spring Q?

• 0.014 m

• 0.038 m

• 0.049 m

• 0.061 m

The diagram shows a uniform metre ruler of weight 1.5 N pivoted 15 cm from one end for use as a simple balance.

A scale pan of weight 0.5 N is placed at the end of the ruler and an object of unknown weight is placed in the pan. The ruler moves to a steady horizontal position when a weight of 2.5 N is added at a distance of 60 cm from the pivot as shown.

What is the weight of the object?

• 9.5 N

• 10.0 N

• 13.0 N

• 13.5 N

A light uniform rigid bar is pivoted at its centre. Forces act on the bar at its ends and at the centre.

Which diagram shows the bar in equilibrium?

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A car bonnet, represented by QP, of mass 12 kg is pivoted at P. Its weight acts at G where QG = GP = 1.0 m.

What force, F, acting perpendicular to QP as shown, is required to hold the bonnet at 30° to the horizontal?

• 29 N

• 51 N

• 59 N

• 136 N

A body of mass 4 kg falls vertically through the air.

What is the acceleration of the body when the magnitude of the air resistance is 30 N?

• 17.3 m s⁻²

• 7.7 m s⁻²

• 2.3 m s⁻²

• .4 m s⁻²

A car wheel nut can be loosened by applying a force of 200 N on the end of a bar of length 0.8 m as in X. A car mechanic is capable of applying forces of 500 N simultaneously in opposite directions on the ends of a wheel wrench as in Y.

What is the minimum length l of the wrench which would be needed for him to loosen the nut?

• 0.16 m

• 0.32 m

• 0.48 m

• 0.64 m

Four rectangular loops of wire A, B, C and D are each placed in a uniform magnetic field of the same flux density B. The direction of the magnetic field is parallel to the plane of the loops as shown.

When a current of 1 A is passed through each of the loops, magnetic forces act on them. The lengths of the sides of the loops are as shown. Which loop experiences the largest couple?

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The diagram shows a vertical square coil whose plane is at right angles to a horizontal uniform magnetic field B. A current, I, is passed through the coil, which is free to rotate about a vertical axis OO'.

Which one of the following statements is correct?

• The forces on the two vertical sides of the coil are equal and opposite.

• A couple acts on the coil.

• No forces act on the horizontal sides of the coil.

• If the coil is turned through a small angle about OO' and released, it will remain in position.

Which line, A to D, in the table shows correctly whether the moment of a force, and momentum, are scalar or vector quantities?

• A

• B

• C

• D