Explanation Given data: Mass of the human sprinter ( m H ) is 70 kg. Mass of the greyhound ( m G ) is 30 kg. The human sprinter can accelerate from rest to 10 m s in 3.0 s. The greyhound can accelerate from rest to 20 m s in 3.0 s. The time period at which both the human sprinter and the greyhound accelerate from the rest to given speeds ( Δ t ) is 3.0 s. Formula used: Refer to the equation (10.23) in the textbook, and write the expression for transformation power as follows. P = Δ E Δ t (1) Here, Δ E is the amount of energy (kinetic energy for the given problem) transformed in a certain time interval, and Δ t is the time interval. Write the expression amount of kinetic energy as follows. Δ E = 1 2 m v 2 (2) Here, m is the mass of the object, and v is the speed (velocity) of the object. Write the expression to find the specific power as follows. specific power = P m (3) Explanation: Calculation of transformation power for the human sprinter ( P H ) : Modify the expression in equation (1) for the transformation power for the human sprinter as follows. P H = ( Δ E ) H Δ t (4) Here, ( Δ E ) H is the amount of energy transformed for the human sprinter in a given time period. Modify the expression in equation (2) for the energy transformed for the human sprinter as follows. ( Δ E ) H = 1 2 m H ( v H ) 2 (5) Here, m H is the mass of the human sprinter, and v H is the speed of the human sprinter after the acceleration period, which is 10 m s . Substitute 70 kg for m H , and 10 m s for v H in equation (5), ( Δ E ) H = 1 2 ( 70 kg ) ( 10 m s ) 2 = 1 2 ( 70 kg ) ( 100 m 2 s 2 ) = 3500 kg ⋅ m 2 s 2 = 3500 J { ∵ 1 kg ⋅ m 2 s 2 = 1 J } Substitute 3500 J for ( Δ E ) H , and 3.0 s for Δ t in equation (4), P H = 3500 J 3.0 s = 1166.6667 J s = 1166.6667 W { ∵ 1 J s = 1 W } Calculation of specific power for the human sprinter: Modify the expression in equation (3) to find the specific power for the human sprinter as follows. ( specific power ) H = P H m H Substitute 1166

College Physics: A Strategic Approach Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition) (What's New in Astronomy & Physics)

4th Edition

ISBN: 9780134641492

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Chapter 10, Problem 66P

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To find: The specific powers for the human sprinter and the greyhound.

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Chapter 10, Problem 65P

Chapter 10, Problem 67P

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T1. Calculate what is the received frequency when the car drives away from the radar antenna at a speed v of a) 1 m/s ( = 3.6 km/h), b) 10 m/s ( = 36 km/h), c) 30 m /s ( = 108 km/h) . The radar transmission frequency f is 24.125 GHz = 24.125*10^9 Hz, about 24 GHz. Speed of light 2.998 *10^8 m/s.

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College Physics: A Strategic Approach Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition) (What's New in Astronomy & Physics)

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