Domanda del libro di testo
A pendulum is made by tying a 500 g ball to a 75-cm-long string. The pendulum is pulled 30° to one side, then released. What is the ball's speed at the lowest point of its trajectory?
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Ch 10: Interactions and Potential Energy
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- 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: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 10, Problema 10
The spring in FIGURE EX10.21a is compressed by 10 cm. It launches a block across a frictionless surface at 0.50 m/s. The two springs in Figure EX10.21b are identical to the spring of Figure EX10.21a. They are compressed by the same 10 cm and launch the same block. What is the block's speed now?
Guida verificata passo dopo passo1
Identify the energy transformation involved: Initially, the potential energy stored in the compressed spring is converted into the kinetic energy of the block as it is launched.
Calculate the initial potential energy stored in the spring using the formula for spring potential energy, PE = 0.5 * k * x^2, where 'k' is the spring constant and 'x' is the compression distance.
Determine the kinetic energy of the block using the formula KE = 0.5 * m * v^2, where 'm' is the mass of the block and 'v' is its velocity. Use the velocity given for the single spring setup to find the kinetic energy.
For the setup with two springs, assume that the potential energy stored in the system when both springs are compressed is twice that of the single spring, since both springs are identical and compressed by the same amount.
Use the conservation of energy principle to equate the total potential energy from the two springs to the kinetic energy of the block and solve for the new velocity 'v' of the block.
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Hooke's Law
Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from the equilibrium position, expressed as F = -kx, where k is the spring constant and x is the displacement. This principle is crucial for understanding how the potential energy stored in a compressed spring is converted into kinetic energy when the spring is released.
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Percorso guidato
05:27
Spring Force (Hooke's Law)
Conservation of Energy
The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the potential energy stored in the compressed spring is converted into kinetic energy of the block as it is launched. This concept allows us to analyze the relationship between the initial and final speeds of the block.
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Percorso guidato
06:24Conservation Of Mechanical Energy
Kinetic Energy
Kinetic energy is the energy possessed by an object due to its motion, calculated using the formula KE = 1/2 mv², where m is the mass and v is the velocity of the object. Understanding kinetic energy is essential for determining how the speed of the block changes when launched by the springs, especially when comparing the effects of multiple springs acting on the same mass.
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Percorso guidato
06:07Intro to Rotational Kinetic Energy
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