What is the tension in the string if the man of mass 80 kg starts climbing up the rope with an acceleration of $3 m / s^{2}$ relative to the rope ? Round off to nearest integer.
$m / s^{2}$

Question

What is the tension in the string if the man of mass 80 kg starts climbing up the rope with an acceleration of 3 m / s 2 relative to the rope ? Round off to nearest integer. m / s 2

TestHub · Accepted Answer

If the 100 kg block stayed at rest, the rope would be stationary and $T = 80 (g + 3) = 1040$ N $> 1000$ N, so the block must lift

Block: $T - 1000 = 100 a_{b}$ ; man: $T - 800 = 80 a$

Rope constraint: the man's acceleration relative to the rope is $a + a_{b} = 3$

Eliminating $a_{b}$ : $T - 1000 = 300 - 100 a$ , and $T - 800 = 80 a$

Subtracting: $a = \frac{25}{9}$ m/s $^{2}$

$T = 800 + \frac{2000}{9} \approx 1022$ N

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