Question

16. A painter in a crate which hangs alongside a building. When the
painter of mass 100 kg pulls the rope, the force exerted by him on the
floor of the crate is 450 N, If the crate weighs 25 kg, find tension in the
rope.​

Answer 1

Answer:

Tension in the rope is 750 N

Explanation:

As we know that the crate will have tension force upwards and painter also having tension force on it

So net upward force on crate and painter is T + T = 2T

So equation of motion of crate + Man is given as

$2T - (M + m)g = (M + m)a$

$2T - (100 + 25)10 = (100 + 25)a$

$T - 625 = 62.5 a$

Now for the man we have three force on him

Upwards force due to crate + Tension force due to rope and downward force is due to weight of the person

so we have

$T + N - Mg = Ma$

$T + 450 - (100)(10) = 100 a$

Now from above two equations we have

$(625 + 62.5 a) - 550 = 100 a$

$75 = 37.5 a$

$a = 2 m/s^2$

Now tension force in the rope is given as

$T = 625 + 62.5(2)$

$T = 750 N$

#Learn

Topic : Newton's Law of motion

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Answer 2

Answer:

Tension in the rope is 750 N

Explanation:

As we know that the crate will have tension force upwards and painter also having tension force on it

So net upward force on crate and painter is T + T = 2T

So equation of motion of crate + Man is given as

2T - (M + m)g = (M + m)a2T−(M+m)g=(M+m)a

2T - (100 + 25)10 = (100 + 25)a2T−(100+25)10=(100+25)a

T - 625 = 62.5 aT−625=62.5a

Now for the man we have three force on him

Upwards force due to crate + Tension force due to rope and downward force is due to weight of the person

so we have

T + N - Mg = MaT+N−Mg=Ma

T + 450 - (100)(10) = 100 aT+450−(100)(10)=100a

Now from above two equations we have

(625 + 62.5 a) - 550 = 100 a(625+62.5a)−550=100a

75 = 37.5 a75=37.5a

a = 2 m/s^2a=2m/s

2

Now tension force in the rope is given as

T = 625 + 62.5(2)T=625+62.5(2)

T = 750 NT=750N