GATE ME 2014 Set 1 — Question 41
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Engineering Mechanics → Statics → Friction & Applications
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Question
A block R of mass 100 kg is placed on a block S of mass 150 kg as shown in the figure. Block R is tied to the wall by a massless and inextensible string PQ. If the coefficient of static friction for all surfaces is 0.4, the minimum force F (in kN) needed to move the block S is
Correct answer
(D) 1.37
Solution
Step 1: Identify the forces acting on block R. The normal force exerted by block S on block R is equal to the weight of block R: N.
Step 2: Calculate the maximum static friction force between block R and block S: N. Since block R is tied to the wall, it remains stationary, and this friction force acts to the left on block S when it tries to move right.
Step 3: Identify the forces acting on block S. The total normal force exerted by the ground on block S is the sum of the weights of both blocks: N.
Step 4: Calculate the maximum static friction force between block S and the ground: N. This force also acts to the left on block S.
Step 5: For block S to just start moving, the applied force must overcome both friction forces: N.
Step 6: Convert the force to kN: kN. The closest option is 1.37.
Step 2: Calculate the maximum static friction force between block R and block S: N. Since block R is tied to the wall, it remains stationary, and this friction force acts to the left on block S when it tries to move right.
Step 3: Identify the forces acting on block S. The total normal force exerted by the ground on block S is the sum of the weights of both blocks: N.
Step 4: Calculate the maximum static friction force between block S and the ground: N. This force also acts to the left on block S.
Step 5: For block S to just start moving, the applied force must overcome both friction forces: N.
Step 6: Convert the force to kN: kN. The closest option is 1.37.
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