2-2 The equilibrium of a system of coplanar forces: practice questions

A uniform ladder rests with its lower end on rough horizontal ground and its upper end against a smooth vertical wall, in a vertical plane perpendicular to the wall. When the ladder is about to slip, the friction force on its lower end acts:

• Ahorizontally towards the wall
• Bhorizontally away from the wall
• Cvertically upwards
• Dalong the ladder towards its upper end

A light beam of length 10 m rests on supports at its two ends. A single load of 200 N hangs at the midpoint. Find the reaction at each support.

• A20 N and 20 N
• B50 N and 150 N
• C100 N and 100 N
• D200 N and 0

A weight W hangs in equilibrium from two vertical strings whose tensions are 25 N and 35 N. Find W.

• A30 N
• B875 N
• C60 N
• D10 N

Two people carry a light pole AB of length 3 m, holding it at the ends A and B. A load of 90 N hangs 1 m from A. Find the force borne by each person.

• A60 N at A, 30 N at B
• B90 N at A, 0 at B
• C30 N at A, 60 N at B
• D45 N at A, 45 N at B

The distance between the wheels of a motorcycle is 1.5 m. Its weight, 200 kg.wt, acts on the vertical line through the midpoint between the wheels, and the rider's weight, 80 kg.wt, acts on the vertical line 0.6 m in front of the rear wheel. Find the reaction of the ground on each wheel.

• Afront 132 kg.wt, rear 148 kg.wt
• Bfront 148 kg.wt, rear 132 kg.wt
• Cfront 140 kg.wt, rear 140 kg.wt
• Dfront 132 kg.wt, rear 68 kg.wt

A light beam AB of length 4 m rests on supports at A and B. A load of 80 N hangs 3 m from A. Find RA and RB.

• ARA = 60 N, RB = 20 N
• BRA = 30 N, RB = 50 N
• CRA = 40 N, RB = 40 N
• DRA = 20 N, RB = 60 N

A light rod AB of length 4 m is hinged at A and carries a load of 60 N at B. It is kept horizontal by a vertical force F applied 1 m from A. Find F.

• A240 N
• B15 N
• C180 N
• D60 N

A uniform rod AB of length 2 m and weight 60 N is hinged at A to a vertical wall and kept horizontal by a light string joining B to a point C on the wall 1.5 m vertically above A. Find the magnitude of the reaction of the hinge.

• A60 N
• B40 N
• C50 N
• D30 N

A light beam AB of length 10 m rests on supports at C and D, where AC = 2 m and DB = 2 m. A load of 100 N hangs at end A. What load hung at end B makes the reaction at C zero (the beam about to tip about D)?

• A400 N
• B100 N
• C800 N
• D25 N

A uniform rod AB of weight 60 N is freely hinged at A and rests in equilibrium inclined at 60° to the horizontal under a horizontal force F acting at B. Find F.

• A10√3 N
• B20√3 N
• C10 N
• D30 N