Assume the elevator is supported by a single ideal cable of...

Assume the elevator is supported by a single ideal cable of fixed length. Forces exerted by the guide rails and air resistance are negligible. A $2010 \mathrm{kg}$ elevator moves with an upward acceleration of $1.50 \mathrm{m} / \mathrm{s}^{2} .$ What is the tension in the cable that supports the elevator?

Assume the elevator is supported by a single ideal cable of fixed length. Forces exerted by the guide rails and air resistance are negligible.
A $2010 \mathrm{kg}$ elevator moves with an upward acceleration of $1.50 \mathrm{m} / \mathrm{s}^{2} .$ What is the tension in the cable that supports the elevator?

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Key Concepts

Newton's Second Law

Newton's second law states that the net force acting on an object is equal to its mass multiplied by its acceleration. This principle allows for the calculation of unknown forces by setting up an equation where the sum of all forces equals the mass times the acceleration.

Free-Body Diagram

A free-body diagram is a graphical illustration used to visualize all the forces acting on one object. It helps in identifying each force, such as gravitational force and tension, which can then be used to set up the equations based on Newton's laws.

Weight (Gravitational Force)

Weight is the force exerted on an object due to gravity, calculated by multiplying the object's mass by the gravitational acceleration. This force is essential in problems involving motion in a gravitational field because it opposes or contributes to the net force acting on the object.

Tension in a Cable

Tension is the force transmitted through a rope or cable that supports or lifts an object. When an object is accelerating upward, the tension in the cable must overcome not only the weight of the object but also provide the additional force required to achieve the acceleration. This concept is directly applied when balancing forces in an accelerating system.

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