A monkey is sitting on a wood plate attached to a rope whose...

A monkey is sitting on a wood plate attached to a rope whose other end is passed over a tree branch, as shown in the figure. The monkey holds the rope and tries to pull it down. The combined mass of the monkey and the wooc plate is $100 . \mathrm{kg} .$ Assume that you can neglect the friction between the rope and the branch. a) What is the minimum force the monkey has to apply to lift itself and the plate off the ground? b) What applied force is needed to move the monkey with an upward acceleration of $2.45 \mathrm{~m} / \mathrm{s}^{2} ?$

A monkey is sitting on a wood plate attached to a rope whose other end is passed over a tree branch, as shown in the figure. The monkey holds the rope and tries to pull it down. The combined mass of the monkey and the wooc plate is $100 . \mathrm{kg} .$ Assume that you can neglect the friction between the rope and the branch.
a) What is the minimum force the monkey has to apply to lift itself and the plate off the ground?
b) What applied force is needed to move the monkey with an upward acceleration of $2.45 \mathrm{~m} / \mathrm{s}^{2} ?$

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Key Concepts

Newton's Second Law

This law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. It is central when analyzing systems in motion, as it allows us to set up equations relating forces, mass, and acceleration, whether the system is at rest (static equilibrium) or accelerating.

Mechanical Advantage in Pulley Systems

Pulley systems change the effective force needed to move an object by redistributing the load across multiple segments of rope. In ideal, frictionless pulleys, this can reduce the applied force required, as the weight is shared between the different segments of the rope.

Static Equilibrium

In a state of static equilibrium, the net forces on a system are zero, which is essential to determine the minimum force just sufficient to overcome gravitational pull without causing acceleration. This concept is used to analyze situations where an object is about to move or is balanced.

Tension in Ropes

Tension refers to the force transmitted through a rope, string, or cable when it is pulled tight by forces acting from opposite ends. In analyzing systems with pulleys, determining the tension is key to understanding how forces are distributed and how much applied force is needed to move or support a load.

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