A 4 kg box is accelerated upwards by a string with a...

A 4 $\mathrm{kg}$ box is accelerated upwards by a string with a breaking strength of 80 $\mathrm{N}$ . What is the maximum upward acceleration that can be applied on the box without breaking the string? (A) 2.5 $\mathrm{m} / \mathrm{s}^{2}$ (B) 5.0 $\mathrm{m} / \mathrm{s}^{2}$ (C) 7.5 $\mathrm{m} / \mathrm{s}^{2}$ (D) 10 $\mathrm{m} / \mathrm{s}^{2}$

A 4 $\mathrm{kg}$ box is accelerated upwards by a string with a breaking strength of 80 $\mathrm{N}$ . What is the maximum upward acceleration that can be applied on the box without breaking the string?
(A) 2.5 $\mathrm{m} / \mathrm{s}^{2}$
(B) 5.0 $\mathrm{m} / \mathrm{s}^{2}$
(C) 7.5 $\mathrm{m} / \mathrm{s}^{2}$
(D) 10 $\mathrm{m} / \mathrm{s}^{2}$

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Key Concepts

Tension Force in a String

Tension is the force exerted along a string, rope, or cable when it is pulled tight by forces acting from opposite ends. In problems involving upward acceleration, the tension in the string must overcome both the gravitational force on the object and provide the additional force required for acceleration. The maximum tension the string can sustain without breaking (its breaking strength) sets a limit on the acceleration that can be applied.

Gravitational Force (Weight)

Gravitational force is the force with which the Earth attracts a body towards its center. It is calculated as the product of the mass of an object and the acceleration due to gravity (mg). This force must be countered by the tension in the string when the object is moved upward.

Newton's Second Law of Motion

This principle states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). It is fundamental in analyzing the motion of objects when forces are applied, including upward accelerations against gravitational forces.

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