Question 4

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is $$0.04$$, the acceleration of the system in m s$$^{-2}$$ is: (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless):

Lets write equations for both the blocks

First for the 6 Kg block

$$mg-T=ma$$

$$6g-T=6a$$

Now for the 20 Kg block

now our frictional force is $$f_l=\mu\ _kN$$

$$f_l=\mu\ _kmg\ $$

$$f_l=0.04\times\ 200$$

$$f_l=8N$$

Now equation for the 20 Kg block is

$$T-f_l=ma$$

$$T-f_l=20a$$

$$6g-T=6a$$

Now ad both equations

$$60-f_l=26a$$

$$60-8=26a=52$$

$$a=2\ \frac{m}{s^2}$$

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