Consider the situation shown in figure (6-E2). Calculate (a) the acceleration of the 1.0 kg blocks, (b) the tension inthe string ocnecting the 1.0 kg blocks and (c) the tensionin th tring attached to 0.50 kg.

Open in App

Solution

From the free body diagrams,
$T + 0.5 a - 0.5 g = 0 μ R + 1 a + T_{1} - T = 0 μ R + 1 a - T_{1} = 0 μ R + a = T_{1}$
From Equation (ii) and (iii) we have

$\Rightarrow R - T_{1} = T_{1} \Rightarrow T = 2 T_{1}$
Equation (ii) becomes $μ R + a + T_{1} - 2 T_{1} = 0 \Rightarrow μ R + a - T_{1} = 0 \Rightarrow T_{1} = μ R + a = 0.2 g + a$

$\Rightarrow T_{1} = \frac{0.5 g - 0.5 a}{2} = 0.25 g - 0.25 a$
From equatons (iv) and (v),
$0.2 g + a = 0.25 g - 0.25 a$

$\Rightarrow a = \frac{0.05}{1.25} \times 10 = 0.4 \times 10 m / s^{2}$
(a) Acceleration of 1 kg block each is 0.4 $m / s^{2}$
(b) Tension, $T_{1} = 0.2 g + a + 0.4 = 2.4 N (c) t = 0.5 g - 0.5 a = 0.5 \times 10 - 0.5 \times 0.4 = 4.8 N$

Suggest Corrections

Similar questions

Q. Consider the situation shown in figure (6−E2). Calculate (a) the acceleration of the 1.0 kg blocks, (b) the tension in the string connecting the 1.0 kg blocks and (c) the tension in the string attached to 0.50 kg.

Figure

Q. Consider the situation shown in figure. Calculate (a) the acceleration of the

1.0 k g

blocks. (b) the tension in the string connecting the

1.0 k g

blocks and (c) the tension in the string attached to

0.50 k g

Q. Consider the situation shown in the figure. Both the pulleys and the string are light and all the surfaces are smooth.
(a) Find the acceleration of 1kg block.
(b) Find the tension in the string.

Q. A system of three blocks are connected by strings as shown in figure. Calculate acceleration of each block and tension in the strings.

Consider the situation shown in figure. All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of the acceleration of the two blocks.

Join BYJU'S Learning Program