A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively:

  • Option 1)

    0.6 and 0.5

  • Option 2)

    0.5 and 0.6

  • Option 3)

    0.4 and 0.3

  • Option 4)

    0.6 and 0.6

 

Answers (1)

As we learnt in

Angle of Friction -

Angle 	heta is called angle of friction.

tan	heta=frac{F_{l}}{R}

tan	heta=mu_{s}

R = Reaction,      frac{F_{l}}{R}=mu_{s}

F_{l}= Force of limiting friction

	heta=tan^{-1}(mu_{s})

- wherein

mu_{s}= static friction coefficient

	heta=Angle made by resultant of limiting friction and R with the normal reaction.

 

 M_{s}=tan\: 30^{\circ}=\: \frac{1}{\sqrt{3}}=\: 0.6

S=ut+\frac{1}{2}at^{2},\ \: \: \: u=0,\ \: \: a=g(sin\theta-Mcos\theta)

4=\frac{1}{2}g (sin 30-M_kcos30)4^{2}

\Rightarrow 0.5\times 10\times \frac{1}{2}-M_k\times 10\times \frac{\sqrt{3}}{2}

\Rightarrow 5\sqrt{3}M_k=4.5\ \: \: \Rightarrow M_k=0.51

Correct option is 1.


Option 1)

0.6 and 0.5

Correct

Option 2)

0.5 and 0.6

Incorrect

Option 3)

0.4 and 0.3

Incorrect

Option 4)

0.6 and 0.6

Incorrect

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