Find the accelerations a_1, a_2 and a_3 of th | vedclass

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(B) Total mass of the system $M = 2\,kg + 3\,kg + 7\,kg = 12\,kg$.Applied force $F = 10\,N$.Maximum static friction between $2\,kg$ and $3\,kg$ blocks

Vedclass · Accepted Answer

$a_1 = a_2 = a_3 = \frac{5}{6}\,m/s^2$

Vedclass · Answer

(B) Total mass of the system $M = 2\,kg + 3\,kg + 7\,kg = 12\,kg$.Applied force $F = 10\,N$.Maximum static friction between $2\,kg$ and $3\,kg$ blocks: $f_{max1} = \mu_1 N_1 = 0.2 	imes 2 	imes 10 = 4\,N$.Maximum static friction between $3\,kg$ and $7\,kg$ blocks: $f_{max2} = \mu_2 N_2 = 0.3 	imes (2+3) 	imes 10 = 15\,N$.Since the force $F = 10\,N$ is applied on the $3\,kg$ block,let's check if the blocks move together. If they move together,the common acceleration is $a = \frac{F}{M} = \frac{10}{12} = \frac{5}{6}\,m/s^2$.For the $2\,kg$ block to move with the system,the required force is $f_1 = m_1 a = 2 	imes \frac{5}{6} = \frac{5}{3} \approx 1.67\,N$. Since $1.67\,N For the $7\,kg$ block to move with the system,the required force is $f_2 = (m_1 + m_2) a = 5 	imes \frac{5}{6} = \frac{25}{6} \approx 4.17\,N$. Since $4.17\,N Thus,all blocks move together with acceleration $a = \frac{5}{6}\,m/s^2$.

Find the accelerations $a_1, a_2$ and $a_3$ of the blocks if a $10\,N$ force $F$ is applied on the $3\,kg$ block as shown in the figure.

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