Ch. 04 - Dynamics: Newton's Laws of Motion

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 04 - Dynamics: Newton's Laws of Motion

Problem 43b

Chapter 4, Problem 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?

Verified step by step guidance

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:

F

_g=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:

F

_g=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 = F

_g.

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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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Related Practice

Textbook Question

An object is hanging by a string from your rearview mirror. While you are accelerating at a constant rate from rest to 28 m/s in 5.0 s, what angle θ does the string make with the vertical? See Fig. 4–46.

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Textbook Question

At the instant a race began, a 65-kg sprinter exerted a force of 720 N on the starting block at a 22° angle with respect to the ground. What was the horizontal acceleration of the sprinter?

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Textbook Question

At the instant a race began, a 65-kg sprinter exerted a force of 720 N on the starting block at a 22° angle with respect to the ground. If the force was exerted for 0.32 s, with what speed did the sprinter leave the starting block?

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Textbook Question

A 27-kg chandelier hangs from a ceiling on a vertical 3.4-m-long wire. What horizontal force would be necessary to displace its position 0.15 m to one side?

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Textbook Question

Determine a formula for the acceleration of the system shown in Fig. 4–49 (see Problem 55) if the cord has a non-negligible mass m_C. Specify in terms of ℓ_A and ℓ_B , the lengths of cord from the respective masses to the pulley. (The total cord length is ℓ_A + ℓ_B.)

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Textbook Question

As shown in Fig. 4–48, five balls (masses 2.00, 2.05, 2.10, 2.15, 2.20 kg) hang from a crossbar. Each mass is supported by '5-lb test' fishing line which will break when its tension force exceeds 22.2 N (5.00lb). When this device is placed in an elevator, which accelerates upward, only the lines attached to the 2.05 and 2.00 kg masses do not break. Within what range is the elevator's acceleration?

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