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Doug uses a 25 N horizontal force to push a 5.0 kg crate up a 2.0-m-high, 20° frictionless slope. What is the speed of the crate at the top of the slope?
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Ch 09: Work and Kinetic 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 9, Problema 41
A 70 kg human sprinter can accelerate from rest to 10 m/s in 3.0 s. During the same time interval, a 30 kg greyhound can go from rest to 20 m/s. What is the average power output of each? Average power over a time interval ∆t is ∆E/∆t.
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Step 1: Start by recalling the formula for average power, which is given as \( P_{avg} = \frac{\Delta E}{\Delta t} \), where \( \Delta E \) is the change in energy and \( \Delta t \) is the time interval.
Step 2: The change in energy \( \Delta E \) is the change in kinetic energy, which can be calculated using the formula \( KE = \frac{1}{2} m v^2 \), where \( m \) is the mass and \( v \) is the velocity. For each case, calculate the final kinetic energy since the initial kinetic energy is zero (starting from rest).
Step 3: For the human sprinter, substitute \( m = 70 \ \text{kg} \) and \( v = 10 \ \text{m/s} \) into the kinetic energy formula: \( KE_{human} = \frac{1}{2} (70) (10)^2 \).
Step 4: For the greyhound, substitute \( m = 30 \ \text{kg} \) and \( v = 20 \ \text{m/s} \) into the kinetic energy formula: \( KE_{greyhound} = \frac{1}{2} (30) (20)^2 \).
Step 5: Divide the calculated kinetic energy for each case by the time interval \( \Delta t = 3.0 \ \text{s} \) to find the average power output: \( P_{avg, human} = \frac{KE_{human}}{3.0} \) and \( P_{avg, greyhound} = \frac{KE_{greyhound}}{3.0} \).
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Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In this scenario, both the sprinter and the greyhound are accelerating, which means their kinetic energy will change as they reach their final speeds. Understanding kinetic energy is essential for calculating the work done and the power output.
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Percorso guidato
06:07
Intro to Rotational Kinetic Energy
Power
Power is defined as the rate at which work is done or energy is transferred over time, expressed mathematically as P = ∆E/∆t. In this context, average power output can be calculated by determining the change in kinetic energy for each athlete and dividing it by the time interval of their acceleration. This concept is crucial for comparing the performance of the sprinter and the greyhound.
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Acceleration
Acceleration is the rate of change of velocity of an object over time, calculated as a = (v_f - v_i)/∆t, where v_f is final velocity, v_i is initial velocity, and ∆t is the time interval. Both the sprinter and the greyhound experience acceleration as they increase their speeds from rest. Understanding acceleration helps in determining the forces involved and the energy changes during their motion.
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Percorso guidato
05:47Intro to Acceleration
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