Moments, levers & gears

The photograph shows a lever-arm balance. The balance can be used to measure the mass of objects to the nearest gram.

The lever-arm is a length of metal, bent at one end as shown in the diagram below. The lever-arm can rotate around the pivot, P.

The arrangement is in equilibrium.

State the two conditions needed for the arrangement to be in equilibrium.

Determine the weight of the counterweight.

Assume the mass of the lever-arm is negligible.

mass of pan = 260 g

An object is placed in the pan. The lever-arm moves along the scale.

Explain why the lever-arm pointer moves through a large distance whilst the pan moves a much shorter distance.

A student uses a digital balance. She sets the balance to zero and then places a prism on the balance, as shown.

A uniform metre rule is pivoted at its 5.0 cm mark. The metre rule is then supported horizontally at the 30.0 cm mark by the prism, as shown below.

The metre rule is in equilibrium.

Explain why the increase in mass recorded by the balance is not equal to the mass of the metre rule.

Calculate the weight of the metre rule. You should take moments about the pivot.

The student wants to reduce the percentage uncertainty in the value obtained for the weight of the metre rule.

The student repeated her determination of the weight of the metre rule. She moved the prism towards the centre of gravity of the metre rule before taking moments about the pivot.

Deduce whether the percentage uncertainty in the value obtained for the weight of the metre rule is reduced by the student moving the prism. No calculations are required.

A film involves a gang of bank robbers making a getaway on a bus loaded with gold bars. The bus spins out of control and ends up balancing on the edge of a cliff, as shown.

State what is meant by the moment of a force about a point.

Overhead electricity cables for railway lines are supported by structures like the one shown.

An electric cable of mass 45 kg is suspended from a support rod X. A second support rod Y is attached to X. X and Y are attached at one end to a column.

The masses of support rods X and Y are negligible.

Determine, by taking moments, the force exerted on rod X by rod Y.

Complete the free‑body force diagram for support rod X.

A website gives a value of the electric field strength E, at two distances from the

Deduce whether these data are consistent with an inverse square law.

The diagrams show the plan view and side view of a moving coil ammeter.

The fixed soft iron cylinder and magnets produce a uniform magnetic field of magnetic flux density B. The coil is able to rotate within this magnetic field. The coil has width w and length l. There is a current I in the coil in the direction shown in the side view diagram.

Explain which way the coil will rotate.

Show that the moment M on the coil about the pivot, due to the magnetic field, is given by

M = BAIN

where A is the cross-sectional area of the coil N is the number of turns of wire on the coil.

An ammeter of this type has a resistance of 625 Ω and will measure a maximum current of 1.6 mA.

The ammeter can be adapted to measure potential difference by adding a resistor in series with the ammeter. This resistor is known as a multiplier.

The ammeter is adapted so that it can measure potential differences up to 5.0 V as shown.

The following multipliers are available:

200 Ω 2500 Ω 3125 Ω 3750 Ω

Deduce which multiplier should be used.

The coil within a very sensitive moving coil ammeter can be damaged when the ammeter is transported. The two ends of the coil are connected together when the ammeter is transported. This reduces the movement of the coil and makes it less likely to be damaged.

A student suggests that this is due to Faraday’s law and Lenz’s law.

Explain how these laws apply to this situation.

A uniform paving slab is to be used as a garden step.

State what is meant by the centre of gravity of an extended body.

A uniform paving slab is to be used as a garden step.

State what is meant by the centre of gravity of an extended body.

The paving slab has a weight of 310 N and a length of 90 cm and will be supported at two points, P and Q, as shown. The distance between P and Q will be 75 cm.

This might be unsafe because a person who places all their weight at the end of the slab might tip the slab.

A person of mass 70 kg stands at the end of the slab.

Deduce whether the slab will tip.

Beam engines contributed to powering the Industrial Revolution in Britain in the 18th century. A beam engine consisted of a beam which could rock to and fro around a well-oiled pivot. Attached to the beam there are two rods, one connected to a piston in a steam cylinder and the other connected to a pump.

The diagram below shows a simplified arrangement of a beam engine.

The beam has a constant thickness and a mass of 3.05 10⁴ kg. The length of the beam is 11.0 m. The pivot P is positioned 6.0 m from the steam cylinder end of the beam.

In its resting position the steam cylinder rod is supported by the base of the steam cylinder with the beam at an angle of 20 to the horizontal.

The steam cylinder rod exerts a force T on the beam. The force exerted on the beam by the pump rod can be neglected.

Calculate the force T.

The engine, which ran continuously, could lift a mass of 2500 kg of water through 12 m each minute. The engine used 1250 kg of coal a day. 1 kg of coal can release 22.3 MJ of energy. The beam engine was said to have an efficiency of 10 %.

Deduce whether this claim for efficiency was correct.

Motors usually have a rotating component which can do work W.

In the diagram below, electric field lines have been drawn around one pair of these spheres.

Add to the diagram to show • the directions of the field lines • the lines of equipotential.

The distance between the centres of each charged sphere in this pair is 5.0 cm.

Show that the force between this pair of charged spheres is about 0.04 N.

charge on each sphere = 0.10 μC

The table shows the typical power and the corresponding angular velocity required for three different appliances.

Deduce which of these appliances, in principle, could use the electrostatic motor in (b).

You should use the word equation in (a) and assume that the length of the rod in the electrostatic motor is 8.0 cm.

Assume that the electrostatic motor would deliver a constant force throughout one complete rotation.