Department of Mechanical Engineering, MITS-FET Name:Engineering Mechanics (ME-105) Tutorial. Batch:Spring Semester 2011-2012 Roll No.:

Engineering Mechanics (ME 105) TUTORIAL SHEET-6

1 Block A of mass 12 kg and block B of mass 6 kg are connected by a string passing over a smooth pulley. If coefficient of friction is 0.12 at all surfaces of contact find smallest value of force P to maintain equilibrium.

2 Can the system in figure be in static equilibrium in the position shown? The uniform bar AB weight 500 N and the weight of block c is 300 N. Friction at A is negligible, and coefficient of static friction is 0.4 at the other two contact surfaces.

3 Determine the minimum horizontal force P required to hold the crate from sliding down the plane. The crate has a mass of 50 kg and the coefficient of static friction between the crate and the plane is ms = 0.25.

4 Crates A and B weigh 200 N and 150 N, respectively. They are connected together with a cable and placed on the inclined plane. If the angle is gradually increased, determine when the crates begin to slide. The coefficients of static friction between the crates and the plane are mA = 0.25 and mB = 0.35.

5 Determine the distance s to which the 90 kg painter can climb without causing the 4 m ladder to slip at its lower end A. The top of the 15 kg ladder has a small roller and at the ground the coefficient of static friction is 0.25. The mass center of the painter is directly above his feet.

6 The man in Fig. is trying to move a packing crate across the floor by applying a horizontal force P. The center of gravity of the 250-N crate is located at its geometric center. Does the crate move if P =60 N? The coefficient of static friction between the crate and the floor is 0.3.

7 Determine the smallest horizontal force P required to lift the 200-kg crate. The coefficient of static friction at all contacting surfaces is 0.3. Neglect the mass of the wedge.

8 Knowing that WA = 25 N and θ = 300, determine a) the smallest value of WB for which the system is in equilibrium, b) the largest value of WB for which the system is in equilibrium

9 Knowing that the coefficient of static friction between the 20-kg block and the incline is 0.30, determine the smallest value of θ for which the block is in equilibrium.

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11 A flexible cable which supports the 100 kg load is passed over a fixed circular drum and subjected to a force P to maintain equilibrium. Value of µ between the cable and the fixed drum is 0.3. (a) For α=0, determine the maximum and minimum values which P may have in order not to raise or lower the load. (b) For P=500 N determine the minimum value which the angle α may have before the load begins to slip.

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14 A 80 kg farmer tries to restrain the cow from escaping by wrapping the rope two turns around the tree trunk as shown. If the cow exerts a force of 1100 N on the rope, determine if the farmer can successfully restrain the cow. The coefficient of static friction between the rope and the tree trunk is 0.15 and between the farmer’s shoes and the ground.

15 A man attempts to support a stack of books horizontally by applying a compressive force of F = 120 N to the ends of the stack with his hands. If each book has a mass of 0.95 kg, determine the greatest number of books that can be supported in the stack. The coefficient of static friction between the man’s hands and a book is 0.6 and between any two books is 0.4.

16 If the coefficient of static friction at the contact points A and B is 0.4, determine the minimum distance d where a 75-lb girl can stand on the plank without causing it to slip. Neglect the weight of the plank.