Theory question 115
Statics(a) A see-saw pivoted at the middle is kept in balance by weights of Richard, John and Philip such that only Richard whose mass is 60 kg sits on one side. If they sit at distances 2m, 3m and 4m respectively from the pivot and Philip is 15 kg, find the mass of John.
(b) A body of mass 12 kg rests on a rough plane inclined at an angle of 30° to the horizontal. The coeffient of friction between the body and the plane is 2/3. A force of magnitude P Newtons acts on the body along the inclined plane. Find the value of P, if the body is at the point of moving: (i) down the plane; (ii) up the plane.
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(a) Moments about the pivot: 60 × 2 = J × 3 + 15 × 4, so 120 = 3J + 60 and John's mass J = 20 kg.
(b) (g = 10) R = 120 cos 30° ≈ 103.9 N; limiting friction = ⅔ × 103.9 ≈ 69.3 N; weight component down the plane = 120 sin 30° = 60 N.
(i) About to move down (friction up the plane): P + 60 = 69.3, P ≈ 9.3 N.
(ii) About to move up (friction down the plane): P = 60 + 69.3 ≈ 129.3 N.
Balance clockwise and anticlockwise moments; friction opposes the motion about to happen.