A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N. If monkey initially climbs down with an acceleration of 4 m/s2 and then climbs up with an acceleration of 5 m/s2. Choose the correct option (g = 10 m/s2).
First, let's analyze the situation when the monkey is climbing down the rope.
The forces acting on the monkey are:
Weight of the monkey: W = mg = 50 \, \text{kg} \times 10 \, \text{m/s}^2 = 500 \, \text{N}
Tension in the rope: T
When climbing down, the monkey experiences a downward acceleration, so the net force equation is:
T = W - ma = mg - ma = m(g - a)
Substituting the values:
T = 50 \times (10 - 4) = 50 \times 6 = 300 \, \text{N}
Since 300 N is less than the breaking tension of 350 N, the rope does not break while climbing down.
Now, let's analyze when the monkey climbs up.
This time, the net force is upward and the equation becomes:
T = W + ma = mg + ma = m(g + a)
Substituting the values:
T = 50 \times (10 + 5) = 50 \times 15 = 750 \, \text{N}
Since 750 N is greater than the breaking tension of 350 N, the rope will break while climbing upward.
Therefore, the correct option is: "Rope will break while climbing upward".
