An elevator weighing 6200 lb is pulled upward by a cable with an acceleration of 3.8 ft / s^2. (

step 1 Hello student in this question it is given mass of elevator left it is represented by graph whic

An elevator weighing 6200 lb is pulled upward by a cable...

An elevator weighing $6200 \mathrm{lb}$ is pulled upward by a cable with an acceleration of $3.8 \mathrm{ft} / \mathrm{s}^{2}$. (a) What is the tension in the cable? (b) What is the tension when the elevator is accelerating downward at $3.8 \mathrm{ft} / \mathrm{s}^{2}$ but is still moving upward?

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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 the mass of the object multiplied by its acceleration (F_net = m * a). This principle is used to relate the forces acting on the elevator—including the gravitational force (weight) and the tension in the cable—to its acceleration, whether upward or downward.

Gravitational Force and Weight

Gravitational force, or weight, is the force exerted on an object due to gravity. It is calculated as the product of the object's mass and the acceleration due to gravity. In problems involving vertical motion, this force opposes or adds to the applied forces such as tension, depending on the direction of acceleration.

Net Force and Direction of Acceleration

Analyzing the net force on an object involves summing all the individual forces considering their directions. In vertical motion, if an object is accelerating upward, the tension in the cable must overcome both the gravitational force and provide the additional upward force (net force). Conversely, if the object is accelerating downward while still moving upward, the applied force (tension) is less than the gravitational force, resulting in a net downward force. This distinction is crucial for setting up the correct equations in solving for tension.

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