A monkey of mass 15 kg is climbing a rope fixed to a ceiling. If it wishes to go up with an acceleration of 1 m/s^{2}, how much force should it apply on the rope? If the rope is 5 m long and the monkey starts from rest, how much time will it take to reach the ceiling?

#### Solution

Mass of the monkey, m = 15 kg,

Acceleration of the monkey in the upward direction, a = 1 m/s^{2}

The free-body diagram of the monkey is shown below:

From the free-body diagram,

T − [15g + 15(a)] = 0

T − [15g + 15(1)] = 0

⇒ T = 5 (10 + 1)

⇒ T = 15 × 11 = 165 N

The monkey should apply a force of 165 N to the rope.

Initial velocity, u = 0

s = 5 m

Using, \[s = ut + \frac{1}{2}a t^2\], we get:

\[5 = 0 + \left( \frac{1}{2} \right) \times 1 \times t^2 \]

\[ \Rightarrow t^2 = 5 \times 2\]

\[ \Rightarrow t = \sqrt{10} s\]

Hence, the time required to reach the ceiling is \[\sqrt{10} s\]