Question

The monkey B, shown in the figure (5−E20), is holding on to the tail of monkey A that is climbing up a rope. The masses of monkeys A and B are 5 kg and 2 kg, respectively. If A can tolerate a tension of 30 N in its tail, what force should it apply on the rope in order to carry monkey B with it? Take g = 10 m/s2.
Figure

Answer 1

Monkey A should exert a force of magnitude between 70 N and 105 N to carry monkey B with it.

Explanation:

Step 1:

Let Monkey A's acceleration upward be a, so that its tail generates a maximum tension of 30 N.

T - 5 g - 30 - 5 a = 0    ...(i)

30 - 2 g - 2 a = 0    ...(ii)

We have: Equations (i) and (ii)

T = 105 N   (max.)

and a = 5 m/$s^2$

Step 2:

A can therefore apply a maximum force of 105 N on the rope to carry with it monkey B.

There is no acceleration of A and B for minimal force.

$T_1$ = mass of monkey B

$T_1$ = 20 N

For monkey A, rewriting equation I we get:

T - 5 g - 20 = 0

T = 70 N

∴ Monkey A should exert a force of magnitude between 70 N and 105 N to carry monkey B with it.

Answer 2

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