The elevator in a hotel has a mass of 750 kg, and it carries six people with a total mass of 45

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The elevator in a hotel has a mass of 750 kg, and it...

The elevator in a hotel has a mass of $750 \mathrm{~kg}$, and it carries six people with a total mass of $450 \mathrm{~kg}$. How much force should the cable pull up with to have an acceleration of $1 \mathrm{~m} / \mathrm{s}^{2}$ in the upward direction?

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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 times its acceleration (F = ma). This principle is essential for calculating the force needed to accelerate a system, as it allows one to determine how much additional force, beyond what is required to counteract gravity, must be applied to achieve a desired acceleration.

Gravitational Force

Gravitational force is the force exerted by gravity on a mass, calculated by multiplying the mass by the gravitational acceleration (approximately 9.8 m/s² on Earth). In the context of the problem, the gravitational force represents the weight that must be overcome in order to lift the elevator and its load, and therefore it is a critical component of determining the total force required.

Net Force and Total Mass

The net force required to accelerate an object upward must account for both overcoming the gravitational pull (i.e., the total weight of the elevator and its contents) and providing the additional force needed to produce acceleration. By combining the masses of the elevator and its occupants into a total mass, one can apply Newton’s Second Law to compute the sum of gravitational force and the force needed for the specified acceleration.

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