91Ó°ÊÓ

The mass of bricks is $m=15\mathrm{kg}$

The mass of counterweight is $M=28\mathrm{kg}$

The acceleration of loads of bricks is calculated by considering the equilibrium of forces in a vertical direction. The tension in each rope is found using acceleration and weights of bricks and counter weight.

The expression for the force is given by,

$F=ma$

Here $m$is the mass, $F$is the force and $a$is the acceleration.

(a)

The free body diagram for bricks load is shown below,

The free body diagram for the counter weight is shown below,

(b)

The upward acceleration of the load bricks is calculated as:

$\left(m+M\right)a=\left(M-m\right)g$

Here, g is the gravitational acceleration and its value is $9.8\mathrm{m}/{\mathrm{s}}^2$.

Substitute $15\mathrm{kg}$for $m$, $28\mathrm{kg}$for $M$and $9.8\mathrm{m}/{\mathrm{s}}^2$ for g in the above equation.

$$\begin{gathered} \left(15\mathrm{kg}+28\mathrm{kg}\right)\mathrm{a}=\left(28\mathrm{kg}-15\mathrm{kg}\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right) \\ \mathrm{a}=2.96\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

Therefore, the upward acceleration of the load of bricks is $2.96\mathrm{m}/{\mathrm{s}}^2$.

(c)

The tension in moving rope is calculated as:

$T=m\left(g+a\right)$

Here, g is the gravitational acceleration and its value is $9.8\mathrm{m}/{\mathrm{s}}^2$, $T$is the tension in the moving rope.

Substitute 15 kg for $m$, $9.8\mathrm{m}/{\mathrm{s}}^2$ for g and $2.96\mathrm{m}/{\mathrm{s}}^2$ for $a$in the above equation.

$$\begin{gathered} T=\left(15\mathrm{kg}\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2+2.96\mathrm{m}/{\mathrm{s}}^2\right) \\ T=191\mathrm{N} \end{gathered}$$

The weight of the bricks is given as:

$$\begin{gathered} w=mg \\ w=\left(15\mathrm{kg}\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right) \\ \mathrm{w}=147\mathrm{N} \end{gathered}$$

The weight of the load of bricks is less than the tension of moving rope.

The weight of the counterweight is given as:

$$\begin{gathered} W=Mg \\ w=\left(28\mathrm{kg}\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right) \\ \mathrm{w}=274\mathrm{N} \end{gathered}$$

The weight of the counterweight is greater than the tension of the moving rope.

Therefore, the tension in the moving rope is 191N .