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Question

A $$50 kg$$ trolley initially moving at a speed of $$15 {m}/{s}$$ along a rail track takes $$20 m$$ to stop with the brakes on.
What is the approximate coefficient of kinetic friction between the tracks and the wheels of the trolley?


A
μ=0.04
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B
μ=0.57
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C
μ=1.14
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D
The situation is impossible
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E
None of the above
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Solution

The correct option is D $$\mu=0.57$$
Given :   $$m = 50$$ kg           $$S = 20$$ m                      $$u = 15$$ m/s                $$v  = 0$$ m/s
Using      $$v^2 - u^2 = 2aS$$
$$\therefore$$   $$0 - (15)^2  = 2 a \times 20$$                              $$\implies a = -5.63$$  $$m/s^2$$

Magnitude of kinetic friction         $$f  = \mu mg$$
$$\therefore$$    $$m|a| = f = \mu mg$$                
$$\implies$$    $$\mu = \dfrac{|a|}{g}  = \dfrac{5.63}{9.8}  = 0.57$$

Physics

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