Question

Figure, shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 ms^-2. What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? 

(Mass of the man = 65 kg.)

Answer 1

Given acceleration of conveyor belt a = 1 ms^-2

µ_s = 0.2 mass of man m = 65 kg

Then man experiences a pseudo force F_s = ma as he is in an accelerating frame as shown in the figure. Hence to maintain his equilibrium he exerts a force F = – F_s = ma = 65 × 1 = 65 N in direction of motion of belt.

∴ Net force acting on man = 65 N The man continue to be stationary with respect to belt if force of friction equal to force acting on man i.e.

µ_s N = ma_max

µ_s . m .g = ma_max

a_(max) = µ_s × g

= 0.2 × 10

= 2ms^-2.