Textbook Question
A 40 kg, 5.0-m-long beam is supported by, but not attached to, the two posts in FIGURE P12.61. A 20 kg boy starts walking along the beam. How close can he get to the right end of the beam without it falling over?
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Ch 12: Rotation of a Rigid Body
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 12, Problem 63b
FIGURE P12.63 shows a 15 kg cylinder held at rest on a 20° slope. What is the magnitude of the static friction force?
Verified step by step guidance1
Identify the forces acting on the cylinder: The forces include the gravitational force (weight), the normal force exerted by the slope, and the static friction force. The weight of the cylinder is given by \( F_g = m \cdot g \), where \( m = 15 \; \text{kg} \) and \( g = 9.8 \; \text{m/s}^2 \).
Resolve the gravitational force into components parallel and perpendicular to the slope. The parallel component is \( F_{g, \parallel} = F_g \cdot \sin(\theta) \), and the perpendicular component is \( F_{g, \perp} = F_g \cdot \cos(\theta) \), where \( \theta = 20^\circ \).
Recognize that the cylinder is at rest, meaning the static friction force must exactly balance the parallel component of the gravitational force. Therefore, \( f_s = F_{g, \parallel} \).
Substitute the expressions for \( F_g \) and \( F_{g, \parallel} \) into the equation for static friction: \( f_s = m \cdot g \cdot \sin(\theta) \).
Plug in the known values for \( m \), \( g \), and \( \theta \) to calculate the magnitude of the static friction force. 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.
Static Friction
Static friction is the force that prevents an object from starting to move when a force is applied. It acts parallel to the surface of contact and varies in magnitude up to a maximum value, which is determined by the coefficient of static friction and the normal force. In this scenario, it is crucial to calculate the static friction force to determine if the cylinder will remain at rest on the slope.
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08:11
Static Friction & Equilibrium
Normal Force
The normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it. On an inclined plane, the normal force is less than the object's weight and can be calculated using the angle of the slope. Understanding the normal force is essential for determining the static friction force acting on the cylinder.
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08:17The Normal Force
Forces on an Incline
When an object is on an inclined plane, the forces acting on it include gravitational force, normal force, and frictional force. The gravitational force can be resolved into components parallel and perpendicular to the slope. Analyzing these forces helps in calculating the static friction force required to keep the object at rest against the pull of gravity down the slope.
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Related Practice
Textbook Question
Blocks of mass m₁ and m₂ are connected by a massless string that passes over the pulley in FIGURE P12.64. The pulley turns on frictionless bearings. Mass m₁ slides on a horizontal, frictionless surface. Mass m₂ is released while the blocks are at rest. Assume the pulley is massless. Find the acceleration of m₁ and the tension in the string. This is a Chapter 7 review problem.
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Textbook Question
A person's center of mass is easily found by having the person lie on a reaction board. A horizontal, 2.5-m-long, 6.1 kg reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A 60 kg woman lies on the reaction board with her feet over the pivot. The scale reads 25 kg. What is the distance from the woman's feet to her center of mass?
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Textbook Question
Your task in a science contest is to stack four identical uniform bricks, each of length L, so that the top brick is as far to the right as possible without the stack falling over. Is it possible, as FIGURE P12.60 shows, to stack the bricks such that no part of the top brick is over the table? Answer this question by determining the maximum possible value of d.
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Textbook Question
Blocks of mass m1 and m2 are connected by a massless string that passes over the pulley in FIGURE P12.64. The pulley turns on frictionless bearings. Mass m1 slides on a horizontal, frictionless surface. Mass m2 is released while the blocks are at rest. Suppose the pulley has mass mp and radius R. Find the acceleration of m1 and the tensions in the upper and lower portions of the string. Verify that your answers agree with part a if you set mp = 0.
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Textbook Question
The 2.0 kg, 30-cm-diameter disk in FIGURE P12.65 is spinning at 300 rpm. How much friction force must the brake apply to the rim to bring the disk to a halt in 3.0 s?