Question

(a) What is the acceleration of the system?
fo) What is the tension at the top of heavy rope?
(c) What is the tension at the mid-point of the rope?
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Answer 1

GIVEN :

• $\sf m_1 \: = \: 5 \: kg$
• $\sf m_2 \: = \: 7 \: kg$
• Mass of rope, m = 4 kg.
• Force, F = 200 Newton.

TO FIND :

1. What is the acceleration of the system?
2. What is the tension at the top of heavy rope?
3. What is the tension at the mid-point of the rope?

FORMULAS USED :

• F = ma.
• T = ma + mg.

SOLUTION :

a) Acceleration of the system, a = ?

Using the equation of force, F = ma.

$\implies \sf F \: - \: mg \: = \: ma$

$\implies \sf 200 \: - \: 16 \: \times \: 10 \: = \: 16 a$

$\implies \sf 200 \: - \: 160 \: = \: 16 a$

$\implies \dfrac {40}{16} \: = \: a$

$\therefore {\boxed {\sf a \: = \: 2.5 \: m/s^{2}}}$

b) Tension at the top of heavy rope = ?

Two mass of blocks,

$\implies \sf m_1 \: + \: m_2$

$\implies \sf 5 \: + \: 4 \: = \: 9 kg$

We know that,

Tension, T = ma + mg.

Taking ‘m’ as common.

$\implies \sf m \: (a \: + \: g)$

$\implies \sf 9 \: \times \: 12.5$

$\therefore {\boxed {\sf T \: = \: 112.5 \: N}}$

c) Tension at the mid-point of rope = ?

Mass of rope = 4 kg.

We know that,

$\implies \sf T \: = \: m \: (a + g)$

$\implies \sf 4 \: \times \: 12.5$

$\therefore {\boxed {\sf T \: = \: 50 \: N}}$