A monkey of mass 20 kg is holding a vertical rope. The rope...

A monkey of mass $20 \mathrm{~kg}$ is holding a vertical rope. The rope can break when a mass of $25 \mathrm{~kg}$ is suspended from it. What is the maximum acceleration with which the monkey can climb up along the rope? (a) $7 \mathrm{~ms}^{-2}$ (b) $10 \mathrm{~ms}^{-2}$ (c) $5 \mathrm{~ms}^2$ (d) $2.5 \mathrm{~ms}^5$

A monkey of mass $20 \mathrm{~kg}$ is holding a vertical rope. The rope can break when a mass of $25 \mathrm{~kg}$ is suspended from it. What is the maximum acceleration with which the monkey can climb up along the rope?
(a) $7 \mathrm{~ms}^{-2}$
(b) $10 \mathrm{~ms}^{-2}$
(c) $5 \mathrm{~ms}^2$
(d) $2.5 \mathrm{~ms}^5$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Tension in the Rope

Tension is the pulling force transmitted along a rope, cable, or string. In this scenario, the rope’s tension increases when the monkey climbs, and it must not exceed the maximum limit that corresponds to a mass of 25 kg (i.e., 25g Newtons) to prevent the rope from breaking.

Free-Body Diagram Analysis

A free-body diagram is a visual representation of the forces acting on a single object, which, in this case, includes the gravitational force pulling the monkey downward and the tension force in the rope pulling it upward. This diagram helps in setting up the equations based on Newton's Second Law to solve for the maximum allowable acceleration without exceeding the tension limit.

Newton's Second Law

Newton's Second Law establishes that the net force on an object is equal to its mass multiplied by its acceleration (F = ma). This principle is used to relate the upward tension force acting on the monkey to both its gravitational force and the additional force required for its acceleration.

Transcript

Please give Ace some feedback