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Ch. 04 - Dynamics: Newton's Laws of Motion
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 04 - Dynamics: Newton's Laws of MotionProblema 43b
Capitolo 4, Problema 43b

A 27-kg chandelier hangs from a ceiling on a vertical 3.4-m-long wire. What will be the tension in the wire?

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1
Identify the forces acting on the chandelier. Since it is hanging at rest, the forces are in equilibrium. The two forces are the gravitational force (weight of the chandelier) acting downward and the tension in the wire acting upward.
Calculate the gravitational force acting on the chandelier using the formula: Fg=mg, where m is the mass of the chandelier (27 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
Substitute the given values into the formula: Fg=27×9.8. This will give the gravitational force in newtons.
Since the chandelier is in equilibrium (not accelerating), the tension in the wire must exactly balance the gravitational force. Therefore, the tension in the wire is equal to the gravitational force: T=Fg.
Conclude that the tension in the wire is numerically equal to the gravitational force calculated in step 3. Ensure the units are in newtons (N).

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Tension in a Wire

Tension is the force exerted along a wire or rope when it is pulled tight by forces acting from opposite ends. In the case of a chandelier hanging from a wire, the tension must counteract the weight of the chandelier to maintain equilibrium. The tension can be calculated using the formula T = mg, where m is the mass and g is the acceleration due to gravity.
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Weight

Weight is the force exerted by gravity on an object, calculated as the product of its mass and the acceleration due to gravity (W = mg). For the chandelier, its weight is the force that the tension in the wire must balance. Understanding weight is crucial for determining the tension in the wire supporting the chandelier.
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Equilibrium

Equilibrium occurs when all the forces acting on an object are balanced, resulting in a state of rest or constant motion. In this scenario, the chandelier is in static equilibrium, meaning the upward tension in the wire equals the downward gravitational force (weight) acting on it. This principle is fundamental in analyzing forces in static systems.
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