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 Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 5, Problem 1a
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?
Verified step by step guidance1
Identify the forces acting on the system: Each weight exerts a downward force of 25.0 N due to gravity. The rope transmits this force to the pulley, creating tension in the rope.
Recognize that the pulley is light and frictionless: This means the tension in the rope is the same on both sides of the pulley, as there is no energy loss or additional forces introduced by the pulley.
Apply the equilibrium condition for the weights: Since the weights are stationary, the upward tension in the rope must exactly balance the downward gravitational force on each weight. Therefore, the tension in the rope on each side is equal to the weight of one of the objects, which is 25.0 N.
Analyze the tension in the rope as a whole: The tension in the rope is uniform throughout because the pulley is frictionless. Thus, the tension in the rope is the same as the force exerted by one of the weights, which is 25.0 N.
Conclude that the tension in the rope is 25.0 N: This is because the system is in equilibrium, and the forces on each side of the rope are balanced.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Tension in a Rope
Tension is the force transmitted through a rope or string when it is pulled tight by forces acting from opposite ends. In a system with weights suspended on either side of a pulley, the tension in the rope is equal to the weight of the objects if they are in equilibrium, meaning they are not accelerating.
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Calculating Tension in a Pendulum with Energy Conservation
Equilibrium
Equilibrium occurs when the net force acting on an object is zero, resulting in no acceleration. In the context of the pulley system, both weights being equal means that the forces balance each other out, allowing us to determine the tension in the rope as equal to the weight of one of the objects.
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Pulley Systems
A pulley system consists of a wheel on an axle or shaft designed to support movement and change the direction of force. In this scenario, the pulley is frictionless, meaning it does not add any additional forces to the system, allowing for a straightforward calculation of tension based solely on the weights involved.
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Related Practice
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.)
Textbook Question
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?
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