# Static Rigid Bodies

A non-uniform plank AB of mass 12kg and length 4 metres is hanging horizontally from two strings C and D. The distances AC and BC are 1 metres and 1.4 metres respectively. A particle of mass 5 kg is placed on the plank at E, 2.4 m away from A. The tensions in the ropes have the same magnitude. What is the first thing that you would write for a question like this?

The reaction at C + the reaction at D = 12g + 5g

Explain how you would do the following question: A uniform plank AB of mass 20kg and length 6m is resting horizontally on two supports at A and C. The distance CB is 1.4 metres. A child of mass 25kg is standing on the plank between C and B, x metres away from B. Find the minimum distance x so the plank will not tilt about C.

Do the question so that the reaction at A = 0, working out the moment about C and then minusing the distance found there from 1.4

If you have a rod and there is a point b which is just in the air, does it have a reaction?

No

Explain how you would solve the following question: 3: A uniform ladder of mass 20 kg and length 8 m rests against a smooth vertical wall with its lower end on rough horizontal ground. The coefficient of friction between the ground and the ladder is 0.3. The ladder is inclined at an angle θ to the horizontal, where tan θ = 2. A boy of mass 30 kg climbs up the ladder. By modelling the ladder as a uniform rod, the boy as a particle and the wall as smooth and vertical, (a) find how far up the ladder the boy can climb before the ladder slips.

P = Fr and R = 50g. Then do the moment around A, making P the subject then subbing in 0.3 x 50g, to work out the distance

A ladder AB, of weight W and length 2l, has one end A resting on rough horizontal ground. The other end B rests against a rough vertical wall. The coefficient of friction between the ladder and the wall is 1/3. The coefficient of friction between the ladder and the ground is μ. Friction is limiting at both A and B. The ladder is at an angle θ to the ground, where tan θ = 5/3. The ladder is modelled as a uniform rod which lies in a vertical plane perpendicular to the wall. Find the value of μ. Start the question (3) and write out the equation for the moment around A

R + Fr against wall = W and R + 1/3P = W and P = Fr of floor. Wcos feta x l = Psin feta x 2l + 1/3P x 2lcos feta

There is a ladder AB of mass 25kg and length 4m, resting in equilibrium with one end A on rough horizontal ground and the other end B against a smooth vertical wall. The ladder is in a vertical plan perpendicular to the wall. The coefficient of friction between the ladder and the ground is 11/25. The ladder makes an angle of alpha with the ground. When Reece, who has made 75kg stands at the point C on the ladder, where AC = 2.8m, the ladder is on the point of slipping. The ladder is modelled as a uniform rod and Reece is modelled as a particle. You answer a load of questions on this, then you are asked to state how you have used the modelling assumption that Reece is a particle, what would you put?

This means that Reece's weight acts at a single point at C