Acceleration of block and trolley system shown in a Figure, if coefficient of kinetic friction betwe

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4-2.Friction

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What is the acceleration of the block and trolley system shown in a Figure, if the coefficient of kinetic friction between the trolley and the surface is $0.04$? What is the tension in the string ? (Take $g = 10\; m s^{-2}$). Neglect the mass of the string.

A$0.96 \;m s ^{-2}\;and\;27.1\;N$

B$0.66 \;m s ^{-2}\;and\;22.5\;N$

C$0.96 \;m s ^{-2}\;and\;12.7\;N$

D$0.48 \;m s ^{-2}\;and\;27.1\;N$

Solution

Answer As the string is inextensible, and the pully is smooth, the $3\, kg$ block and the $20 \,kg$ trolley both have same magnitude of acceleration. Applying second law to motion of the block (Fig. $5.12( b ))$ $30-T=3 \,a$
Apply the second law to motion of the trolley
$T-f_{ k }=20 \,a$
Now $\quad f_{k}=\mu_{k} N$
Here $\mu_{k} =0.04$
$N =20 \times 10$
$=200\, N$
Thus the equation for the motion of the trolley is $T-0.04 \times 200=20 \,a$ Or $T-8=20 \,a$
These equations give $a=\frac{22}{23} \,m s ^{-2}=0.96 \;m s ^{-2}$
and $T=27.1 \,N$

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Solution

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