Textbook Question
Two -N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain from the ceiling. What is the tension in the chain?
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Ch 05: Applying Newton's Laws
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 5, Problem 3b
A -kg wrecking ball hangs from a uniform, heavy-duty chain of mass kg. What is the tension at a point three-fourths of the way up from the bottom of the chain?
Verified step by step guidance1
Identify the forces acting on the chain and the wrecking ball. The tension at any point in the chain must support the weight of the wrecking ball and the portion of the chain below that point. Use the concept of distributed weight for the chain and treat the wrecking ball as a point mass.
Calculate the total weight of the wrecking ball using the formula: , where is the mass of the wrecking ball (75.0 kg) and is the acceleration due to gravity (9.8 m/s²).
Determine the weight of the chain below the point three-fourths of the way up. The chain has a total mass of 26.0 kg, so the mass of the chain below this point is one-fourth of the total chain mass. Use the formula: , where is the mass of the chain below the point.
Add the weight of the wrecking ball and the weight of the chain below the point to find the total force that the tension must support at this location. Use the formula: .
Substitute the known values into the equations and simplify to find the tension at the specified point. Ensure that the units are consistent throughout the calculation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Tension in a Chain
Tension is the force exerted along the length of a chain or rope when it is subjected to a load. In this scenario, the tension varies along the chain due to the weight of the chain itself and the wrecking ball. The tension at any point in the chain can be calculated by considering the weight of the chain below that point and any additional loads acting on it.
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Weight and Mass
Weight is the force exerted by gravity on an object, calculated as the product of its mass and the acceleration due to gravity (approximately 9.81 m/s² on Earth). In this problem, both the wrecking ball and the chain have mass, and their combined weight contributes to the tension experienced at different points in the chain.
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Static Equilibrium
Static equilibrium occurs when an object is at rest and the sum of all forces acting on it is zero. In this context, the wrecking ball and the chain are in static equilibrium, meaning the upward tension forces must balance the downward gravitational forces. Understanding this principle is crucial for analyzing the forces at play in the system.
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Related Practice
Textbook Question
Two -N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain from the ceiling. What is the tension in the rope?
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Textbook Question
Find the tension in each cord in Fig. E if the weight of the suspended object is .
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Textbook Question
A large wrecking ball is held in place by two light steel cables (Fig. E). If the mass m of the wrecking ball is kg, what are the (a) tension in the cable that makes an angle of with the vertical and (b) the tension in the horizontal cable?
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Textbook Question
A picture frame hung against a wall is suspended by two wires attached to its upper corners. If the two wires make the same angle with the vertical, what must this angle be if the tension in each wire is equal to of the weight of the frame? (Ignore any friction between the wall and the picture frame.)