Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 3, Problem 50P
To determine

The additional power needed to achieve the acceleration.

The additional power needed to achieve the acceleration when the total mass of the car is 700kg.

Expert Solution & Answer
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Explanation of Solution

Given:

Mass of the car (mcar) is 1400kg.

Initial speed of the car (V1) is 70km/h.

Final speed of the car (V2) is 100km/h.

Change in time interval of the car (Δt) is 5s.

Acceleration due to gravity (g) is 9.81m/s2.

Calculation:

Calculate the additional power needed to achieve the acceleration (W˙in) using the energy balance equation.

  E˙inE˙out=dEsystem/dtE˙in0=dEsystem/dt

  E˙in=dEsystem/dt=ΔEsysΔt

  W˙in=ΔKEΔt

  W˙in=m(V22V12)2Δt=(1400kg)[(110km/h)2(70km/h)2]2(5s)=(1400kg)[(110×518m/s)2(70×518m/s)2]2(5s)(1kJ/kg1000m2/s2)=77.8kJ/s(1kW1kJ/s)=77.8kW

Thus, the additional power needed to achieve the acceleration is 77.8kW_.

Calculate the additional power needed to achieve the acceleration (W˙in) when the total mass of the car is 700kg.

  W˙in=m(V22V12)2Δt

  W˙in=(700kg)[(110km/h)2(70km/h)2]2(5s)=(700kg)[(110×518m/s)2(70×518m/s)2]2(5s)(1kJ/kg1000m2/s2)=38.9kJ/s(1kW1kJ/s)=38.9kW

Thus, the additional power needed to achieve the acceleration is 38.9kW_.

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Chapter 3 Solutions

Fundamentals of Thermal-Fluid Sciences

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