Textbook Question
You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. How much time does it take the pendulum bob to reach its highest speed?
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Ch 14: Periodic Motion
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 14, Problem 29e
A 0.500-kg glider, attached to the end of an ideal spring with force constant k = 450 N/m, undergoes SHM with an amplitude of 0.040 m. Compute the total mechanical energy of the glider at any point in its motion
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Understand that the total mechanical energy in simple harmonic motion (SHM) is the sum of kinetic and potential energy, but it remains constant throughout the motion.
The total mechanical energy (E) in SHM can be calculated using the formula: E = (1/2) * k * A^2, where k is the spring constant and A is the amplitude of the motion.
Substitute the given values into the formula: k = 450 N/m and A = 0.040 m.
Calculate the expression: E = (1/2) * 450 * (0.040)^2.
This calculation will give you the total mechanical energy of the glider at any point in its motion.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Simple Harmonic Motion (SHM)
Simple Harmonic Motion is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. In SHM, objects oscillate around an equilibrium position, and the motion is characterized by sinusoidal patterns. Understanding SHM is crucial for analyzing the motion of the glider attached to the spring.
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Simple Harmonic Motion of Pendulums
Hooke's Law
Hooke's Law states that the force exerted by a spring is proportional to the displacement from its equilibrium position, expressed as F = -kx, where k is the spring constant and x is the displacement. This law is essential for calculating the potential energy stored in the spring, which contributes to the total mechanical energy of the system.
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05:27Spring Force (Hooke's Law)
Total Mechanical Energy in SHM
The total mechanical energy in SHM is the sum of kinetic and potential energy, which remains constant throughout the motion. For a spring-mass system, it is given by E = (1/2)kA^2, where k is the spring constant and A is the amplitude. This formula allows us to compute the total energy of the glider at any point in its oscillation.
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Related Practice
Textbook Question
A 0.500-kg glider, attached to the end of an ideal spring with force constant k = 450 N/m, undergoes SHM with an amplitude of 0.040 m. Compute the speed of the glider when it is at x = -0.015 m.
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Textbook Question
A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat, the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies when the cat is at its highest point.
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Textbook Question
A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?
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Textbook Question
A small block is attached to an ideal spring and is moving in SHM on a horizontal frictionless surface. The amplitude of the motion is 0.165 m. The maximum speed of the block is 3.90 m/s. What is the maximum magnitude of the acceleration of the block?
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Textbook Question
A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. The amplitude of the motion is 0.250 m and the period is 3.20 s. What are the speed and acceleration of the block when x = 0.160 m?
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