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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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 1b
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?
Verified step by step guidance1
Step 1: Begin by analyzing the forces acting on the pulley. The pulley is in equilibrium, meaning the net force acting on it is zero. The tension in the chain must balance the combined forces exerted by the two weights.
Step 2: Each weight exerts a force of 25.0 N downward due to gravity. Since the rope is frictionless and the pulley is light, the tension in the rope is the same on both sides of the pulley.
Step 3: The total downward force exerted on the pulley is the sum of the tensions from both sides of the rope. This is given by \( F_{total} = T_{rope} + T_{rope} \), where \( T_{rope} \) is the tension in the rope caused by each weight.
Step 4: Substitute the value of \( T_{rope} \) (which is equal to the weight of each object, 25.0 N) into the equation. The total downward force becomes \( F_{total} = 25.0 \text{ N} + 25.0 \text{ N} \).
Step 5: The tension in the chain must equal the total downward force to maintain equilibrium. Therefore, the tension in the chain is equal to \( F_{total} \).
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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 this scenario, the tension in the rope is equal to the weight of the objects suspended, as they are in equilibrium. Since both weights are equal, the tension in the rope will be the same as the weight of one of the objects.
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Equilibrium
Equilibrium occurs when all the forces acting on an object are balanced, resulting in no net force and no acceleration. In this case, the two weights are equal and opposite, leading to a state of equilibrium. This principle allows us to analyze the forces in the system and determine the tension in the chain.
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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 problem, the frictionless pulley allows the weights to move freely without resistance, simplifying the analysis of forces. The tension in the chain must support the total weight of the system, which is crucial for calculating the tension.
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Related Practice
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.)
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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