1. A system consisting of two blocks connected by a cable is as shown in figure. The masses of the block A and block B are 7.5 kg and 25 kg respectively. Determine the magnitude of minimum force and its inclination with reference to the horizontal, to be applied on block B. The block have impending motion towards the right. Take the coefficient of friction at all contact surfaces to be 0.28.

2. A body which weights 1000 N rests on a horizontal plane, the co-efficient of friction between the body and the plane being 0.1. Find the force, which acting at 30° to the horizontal will just move the body. [Ans. 109.2 N]

3. A body resting on a rough horizontal plane required a pull of 82 N inclined at 30° to the plane just to move it. It was found that a push of 100 N inclined at 30° to the plane just moved the body. Determine the weight of the body and the co-efficient of friction. [Ans. 455 N, μ = 0.1714]

4. A 100 N mass is dragged by a rope up 10° slope, the rope being paralleled to the line of the sleepest slope. The co-efficient of friction is 0.5. Calculate the tension in the rope. [Ans. 66.9 N]

5. A body is in equilibrium on an inclined plane. Show clearly by means of a diagram, the forces acting on the body, describing the forces e.g., weight etc. The inclination of the plane is increased and it is found that uniform motion, once started, continues when the plane is inclined at 15° to the horizontal. What is the co-efficient of friction between the body and the plane ? What force parallel to the plane, will be required to keep the body, whose weight is 100 N at rest when the plane is inclined at 30° to the horizontal? [Ans. 0.268, 26.8 N]

6. A uniform ladder rests with one end on a horizontal floor and the other end against a wall, the coefficients of friction for the floor and wall are 4/9 and 1/4 respectively. Find the inclination of the ladder when it is about to slip. [Ans. 45°]

7. A ladder 5 m long and of 250 N weight is placed against a vertical wall in a position where its inclination to the vertical is 30°. A man weighing 800 N climbs the ladder.

At what position will be induce slipping, the co-efficient of friction for both the contact surfaces of the ladder viz with the wall and floor is 0.2.[Ans. 1.79 m]

8. A uniform ladder 3 m long weighs 200 N. It is placed against a wall making an angle of 60° with the floor. The co-efficient of friction between the wall and the ladder is 0.25 and that between the floor and ladder is 0.5. The ladder in addition to its own weight has to support a man weighing 1 kN its top. Calculate.(i) The horizontal force P to be applied to the ladder at the floor level to prevent

slipping.(ii) If the force P is not applied, what should be the maximum inclination of the ladder

with the horizontal so that there is no slipping of it with the man at top. [Ans. 183.6 N, 68° 57′]

9. The 20-lb block A and the 30-lb block B are supported by an incline that is held in the position shown. Knowing that the coefficient of static friction is 0.15 between the two blocks and zero between block B and the incline, determine the value of µ for which motion is impending.

10.The 15-ft ladder has a uniform weight of 80 lb and rests against the smooth wall at B. If the coefficient of static friction at A is determine if the ladder will slip.Take ө = 60°. µA = 0.4,

11.The three bars have a weight of and respectively. If the coefficients of static friction at the surfaces of contact are as shown, determine the smallest horizontal force P needed to move block A.WC = 60 lb, WA = 20 lb, WB = 40 lb,