Question

Find the accelerations a1, a2, a3 of the three blocks shown in figure (6−E8) if a horizontal force of 10 N is applied on (a) 2 kg block, (b) 3 kg block, (c) 7 kg block. Take g = 10 m/s2.
Figure

Answer 1

Explanation:

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Answer 2

Explanation:

In the question, it is given:

$\mu 1=0.2 ; \mu 2=0.3 ; \mu 3=0.4$

As per the figure:

(a) The frictional force is experienced on the 2 kg block when the 10 N force is applied. Here,

$\mu 1 R 1=m 1 g x \mu 1=(0.2) \times 20=4 N$          

2kg block experiences the net force = $10-4=6 N$.

Therefore, $a 1=3 m / s^{2}$

From the 2 kg block, the frictional force is 4 N. But for the 3 kg block (Fig. 3), it becomes the driving force.

The maximum frictional force among the 7 kg and 3 kg blocks.

So, we have $\mu 2=\mu^{2} m^{2} g=R 2=(0.3) \times 5 \mathrm{kg}$

= 15 N

Therefore, relative to the 7 kg block, the 3 kg block cannot move.

The 7 kg block and the 3 kg block have the equal acceleration $(a 2=a 3)$, which is because of the 4 N force as from the floor, there is no friction.

Therefore $a 2=410=a 3=0.4 \mathrm{m} / \mathrm{s}^{2}$

(b) To the 3 kg block, when the 10 N force is exerted, it includes maximum frictional force of 19 N, from the 7 kg block and the 2 kg block.

So, with respect to them, it cannot move.    

Therefore $a 1=a 3=a 2=56 \mathrm{m} / \mathrm{s}^{2}$

(c) Likewise, it is proven that to the 7 kg block, when the 10 N force is applied, all three blocks transfer with the equal acceleration.

Therefore $a 1=a 3=a 2=56 \mathrm{m} / \mathrm{s}^{2}$.