Tension

Step 1: Climbing upward The tension in the rope during upward motion is calculated using the formula: where: (mass of the monkey), (gravitational acceleration), (acceleration while climbing upward). Substituting the values: Since the tension exceeds the rope's breaking strength ( ), the rope will break during upward motion.

Step 2: Climbing downward The tension in the rope during downward motion is given by: where (acceleration while climbing downward). Substitute the values: Here, the tension is less than the breaking strength ( ), so the rope will not break during downward motion.

Final Answer:

Concepts:

Newton's second law, Tension, Free body diagram

Explanation:

To find the tension in the rope at the fixed support, we need to consider the forces acting on each monkey separately and then sum the tensions. For the monkey climbing up, we use Newton's second law to find the tension in the rope. For the monkey coming down with uniform velocity, the tension is equal to its weight since there is no acceleration.

Step by Step Solution:

Step 1

Identify the forces acting on the monkey climbing up (mass = 10 kg, acceleration = 2 m/s^2).

Step 2

Using Newton's second law, the net force on the climbing monkey is given by:

where is the tension in the rope, is the mass of the monkey, is the acceleration due to gravity (9.8 m/s^2), and is the acceleration.

Step 3

Rearrange the equation to solve for :

Step 4

Identify the forces acting on the monkey coming down with uniform velocity (mass = 8 kg). Since the monkey is moving with uniform velocity, there is no acceleration, and the tension is equal to the weight of the monkey:

Step 5

The total tension in the rope at the fixed support is the sum of the tensions due to both monkeys:

Step 6

Calculate the total tension:

Final Answer:

The tension in the rope at the fixed support is 196.4 N.