An engineer is designing a conveyor system for loading lay bales into a wagon. Each bale is 0.25 m wide, 0.50 m high, and 0.80 m long (the dimension perpendicular to the plane of the figure), with mass 30.0 kg.
Fig.
The centre of gravity of each bale is at its geometrical center. The coefficient of static friction between a bale and the conveyor belt is 0.60, and the belt moves with constant speed. The angle β of the conveyor is slowly increased. At some critical angle a bale will tip (if it doesn't slip first), and at some different critical angle it will slip (if it doesn't tip first).
(i) Find the first critical angle (In the same conditions) at which it tips –
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) : In critical case, normal reaction will shift to extreme left edge.
Fig.
f = mg sin β and
N = mg cos β
In this case τ t = t N (about C)
or f 
= N × 
or 2 mg sin β = mg cos β
or tan β = 0.5
or β = tan –1 (0.5)
(ii) : mg sin β = µ s mg cos β
or tan β = µ s = 0.6
∴ β = tan –1 (0.6)
(iii) : β = tan –1 0.50
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