(a) A body of mass 5 kg is placed on a smooth plane inclined at an angle 30° to the horizontal. Find the magnitude of the force: (i) acting parallel to the plane (ii) required to keep the body in equilibrium. [Take g = (10 ms^{-2})].
(b) A uniform plank PQ of length 10m and mass m kg rests on two supports A and B, where |PA| = |BQ| = 1m. A load of mass 8 kg is placed on the plank at point C such that |AC| = 3.5 m. If the reaction at B is 100 N, calculate the (i) value of m (ii) reaction at A. [Take g = (10 ms^{-2})].
Explanation
(a)
(i) Force parallel to plane = (mg sin 30)
= (5 times 10 times 0.5 )
= (25 N)
(ii) Force required to keep the body in equilibrium
= (mg sin 30 – mu R)
= (25 – mu times 5 times frac{5sqrt{3}}{2})
= (25(1 – mu) frac{sqrt{3}}{2})
b)
Since the plank does not move, all forces and torques are balanced. Forces:
RA + RB – mCg – mpg=0,
torques (consider A as the pivot):
(frac{mp}{10})g ⋅ 0.5 − (frac{9}{10})mpg⋅4.5 −mCg⋅3.5+100⋅8=0
mp=13 kg,
RA=110 N.