Moments of forces, equilibrium of rods and beams, centres of mass of uniform rods, tilting, reactions at supports, non-uniform rods.
12 original questions, 84 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
A uniform beam AB has length 4 m and mass 12 kg. The beam rests horizontally on two supports, one at C and one at D, where AC = 0.5 m and DB = 1 m, as shown in the diagram.
Find the magnitude of the reaction on the beam at C and the magnitude of the reaction on the beam at D.
A uniform plank PQ has length 6 m and mass 20 kg. The plank is held in a horizontal position by two light vertical ropes, one attached at P and one attached at the point R on the plank, where PR = 5 m. A bucket of mass 5 kg hangs from the end Q. The bucket is modelled as a particle.
Find the tension in each rope.
A non-uniform plank AB has length 3.6 m and mass 15 kg. The plank hangs in a horizontal position from two light vertical strings, one at A and one at B. The tension in the string at B is one and a half times the tension in the string at A.
A uniform plank AB has length 5 m and mass 30 kg. It rests horizontally on two supports at C and D, where AC = 1 m and DB = 1.5 m, as shown in the diagram. A child of mass 12 kg stands on the plank at B. The child is modelled as a particle.
The child gets off and an adult of mass M kg stands at B. The plank is now on the point of tilting about D.
A uniform rod AB has length 4 m and mass 10 kg. The rod rests horizontally on two supports at C and D, where AC = 1 m and AD = 2.5 m. A particle of mass 15 kg is placed on the rod at the point P, where AP = x metres.
Given that the rod remains in equilibrium, find the range of possible values of x.
A diving board AB is modelled as a uniform rod of length 4 m and mass 40 kg. The end A is bolted to the ground and the board rests horizontally on a support at C, where AC = 1 m, as shown in the diagram. A diver of mass 60 kg stands at the end B. The diver is modelled as a particle.
A uniform rod AB has length 2a and weight W. The rod rests horizontally on two supports, one at A and one at C, where AC = 32a. A particle of weight kW is attached to the rod at B, where k is a constant.
A non-uniform rod AB has length 3 m. When the rod rests on a single support at the point C, where AC = 1.2 m, it balances in a horizontal position. A particle of mass 2 kg is now attached to the rod at B, and the rod now balances horizontally when the support is moved to the point D, where AD = 1.5 m.
A uniform rod AB has length 2 m and mass 5 kg. The end A is freely hinged to a vertical wall. The rod is held in a horizontal position by a light inextensible string. One end of the string is attached to the rod at B and the other end is attached to the wall at the point C, vertically above A. The string makes an angle of 30° with the rod, as shown in the diagram.
A non-uniform beam AB has length 6 m and mass 50 kg. The beam rests horizontally on two supports at C and D, where AC = 1 m and DB = 2 m. When a woman of mass 30 kg stands on the beam at B, the beam is on the point of tilting about D. The woman is modelled as a particle.
The woman now walks along the beam and stands at A.
A uniform ladder AB has length 6 m and mass 20 kg. The ladder rests with its end A on rough horizontal ground and its end B against a smooth vertical wall. The ladder makes an angle of 60° with the ground and lies in a vertical plane perpendicular to the wall, as shown in the diagram. The ladder is modelled as a uniform rod.
The coefficient of friction between the ladder and the ground is in fact 0.35. A man of mass 75 kg climbs slowly up the ladder. The man is modelled as a particle.
A uniform rod AB has length 4 m and weight W. The rod rests with its end A on rough horizontal ground and rests against a small smooth peg at the point C on the rod, where AC = 3 m. The rod is in a vertical plane perpendicular to the peg and makes an angle θ with the ground, where tan θ = 34, as shown in the diagram. The rod is in limiting equilibrium.
Answer the questions above and your score appears here.
Every question here is original and written by Robinson Tuition. It follows the Edexcel AS specification and suits AQA and OCR AS maths too; this is not an exam-board paper.