The concepts in this problem are similar to those in...

The concepts in this problem are similar to those in Multiple-Concept Example 4, except that the force doing the work in this problem is the tension in the cable. A rescue helicopter lifts a $79-\mathrm{kg}$ person straight up by means of a cable. The person has an upward acceleration of $0.70 \mathrm{m} / \mathrm{s}^{2}$ and is lifted from rest through a distance of $11 \mathrm{m}$. (a) What is the tension in the cable? How much work is done by (b) the tension in the cable and (c) the person's weight? (d) Use the work-energy theorem and find the final speed of the person.

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Key Concepts

Newton's Second Law

This principle relates the net force acting on an object to its mass and acceleration (F_net = m*a). It is used to determine the forces (such as tension and gravitational force) acting on the system when the object accelerates.

Work Done by a Force

Work is defined as the product of the force applied, the displacement in the direction of the force, and the cosine of the angle between them. This concept is used to calculate the work done by both the tension in the cable and the gravitational force acting on the object.

Gravitational Force

This is the force exerted by the Earth on a mass, calculated as the product of the mass and the acceleration due to gravity (mg). It is crucial for determining the net force on the object as well as the work done by the weight during the lift.

Work-Energy Theorem

This theorem states that the net work done on an object equals its change in kinetic energy. It is key to linking the work done by forces acting on an object to its final speed, especially when movement involves acceleration from rest.

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