one end of a light inextensible string is attached to a tool box of mass 2.5 kg which is lying on a horizontal table.
the string passing over a smooth pulley and is tied at other and to bag of mass 1.4kg
a) draw a diagram showing the forces acting on the toolbox
b) is the toolbox is just on the point of sliding find the value for omega the coefficient of friction
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Answer: coefficient of friction μ = 0.56
Explanation:
When the tool box is at the point of sliding, the system is in static equilibrium due to Weight bag and maximum frictional force.
Consider bag as a system :
Tension T = wt of bag = 1.4 x 10 = 14 N
Consider Tool box as system :
For vertical equilibrium :
Normal reaction R = wt of tool box = 2.5 x 10 = 25 N
For horizontal equilibrium :
Max static frictional force = T
f = T
μR = 14
μ = 14/25
= 0.56
∴ coefficient of friction μ (or ω) = 0.56
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