Moments

– 2 18 In this question use g = 9.81 m s

A uniform platform AD has length 2.5 metres and weight 400 newtons.

The platform is attached to a chain at A. The other end of the chain is fixed to the floor.

The platform rests on a support at a point B which is 0.6 metres from A

The support exerts an upwards reaction force on the platform.

A child of mass 30 kilograms stands at a point C

The point C is 0.2 metres from D, as shown in the diagram.

The system is in equilibrium with the platform resting horizontally.

By taking moments about A, find the reaction force at B

The child moves from C to B

State what happens to the reaction force at B during this movement.

Having reached B, the child steps off the platform.

State what happens to the tension in the chain during this movement.

A uniform plank PQ, of length 7 metres, lies horizontally at rest, in equilibrium, on two fixed supports at points X and Y

The distance PX is 1.4 metres and the distance QY is 2 metres as shown in the diagram below.

The reaction force on the plank at X is 4 g newtons.

Show that the mass of the plank is 9.6 kilograms.

Find the reaction force, in terms of g, on the plank at Y

The support at Y is moved so that the distance QY 1.4 metres.

The plank remains horizontally at rest in equilibrium.

It is claimed that the reaction force at Y remains unchanged.

Explain, with a reason, whether this claim is correct.

A £2 coin has a diameter of 28 mm and a mass of 12 grams.

A uniform rod AB of length 160 mm and a fixed load of mass m grams are used to check that a £2 coin has the correct mass.

The rod rests with its midpoint on a support.

A £2 coin is placed face down on the rod with part of its curved edge directly above A.

The fixed load is hung by a light inextensible string from a point directly below the other end of the rod at B, as shown in the diagram.

Given that the rod is horizontal and rests in equilibrium, find m.

State an assumption you have made about the £2 coin to answer part (a).

A straight uniform rod, AB, has length 6 m and mass 0.2 kg

A particle of weight w newtons is fixed at A.

A second particle of weight 3 w newtons is fixed at B.

The rod is suspended by a string from a point x metres from B.

The rod rests in equilibrium with AB horizontal and the string hanging vertically as

Show that

A uniform rod, AB, has length 7 metres and mass 4 kilograms.

The rod rests on a single fixed pivot point, C, where AC 2 metres.

The system is in equilibrium with the rod resting horizontally.

Find W, giving your answer in terms of g.

Explain how you have used the fact that the rod is uniform in part (a).

A metal rod, of mass m kilograms and length 20 cm, lies at rest on a horizontal shelf.

The end of the rod, B, extends 6 cm beyond the edge of the shelf, A, as shown in the diagram below.

The rod is in equilibrium when an object of mass 0.28 kilograms hangs from the midpoint of AB.

The object of mass 0.28 kilograms is removed.

A number, n, of identical objects, each of mass 0.048 kg, are hung from the rod all at a distance of 1 cm from B.

Find the maximum value of n such that the rod remains horizontal.

State one assumption you have made about the rod.

A uniform rod, AB, has length 4 metres. The rod is resting on a support at its midpoint C. A particle of mass 4 kg is placed 0.6 metres to the left of C. Another particle of mass 1.5 kg is placed x metres to the right of C, as shown.

The rod is balanced in equilibrium at C.

Find x.

Circle your answer.

1.8 m 1.5 m 1.75 m 1.6 m