One of the first things you learn in physics class is the law of universal gravitation.
(a)
S.I. unit of
Answer to Problem 74P
S.I. unit of
Explanation of Solution
Expression for gravitational force,
Here, the gravitational constant is
Dimensional formula for
Here, dimension of mass is
Dimensional formula for mass,
Dimensional formula for
Calculation:
Rearrange the Equation (I) for
Substitute
Conclusion:
Therefore, the S.I unit of
(b)
The non dimensional expression for
Answer to Problem 74P
The required expression is
Explanation of Solution
Write the expression for number of
Here, the number of variables are
Substitute
Therefore, the number of
Write the expression for first
Write the expression for the second
Calculation:
The dimensional formula for
Substitute
Compare the exponential coefficient of
Compare the exponential coefficient of
Compare the exponential coefficient of
Substitute
Substitute
Compare the exponential coefficient of
Compare the exponential coefficient of
Compare the exponential coefficient of
Substitute
From Equation (VII) and Equation (IX).
Here, the constant is
Substitute
Conclusion:
The required expression is
(c)
The functional relation between
Answer to Problem 74P
Any functional relation is possible between the two pi terms.
Explanation of Solution
Write the expression for the first pi term.
Write the expression for the second pi term.
Calculation:
Substitute
Substitute
Conclusion:
Any functional relation is possible between the two pi terms.
Want to see more full solutions like this?
Chapter 7 Solutions
Fluid Mechanics: Fundamentals and Applications
- The gravitational constant g is 9.807 m/s² at sea level, but it decreases as you go up in elevation. A useful equation for this decrease In g is g= a - bz, where z is the elevation above sea level, a = 9.807 m/s², and b=3.32 x 10-61/s². An astronaut "weighs" 80.0 kg at sea level. [Technically this means that his/her mass is 80.0 kg.] Calculate this person's weight in N while floating around in the International Space Station (z=325 km). If the Space Station were to suddenly stop in its orbit, what gravitational acceleration would the astronaut feel Immediately after the satellite stopped moving? The person's weight in N while floating around in the International Space Station Is The astronaut feels a gravitational acceleration of m/s² N.arrow_forwardMechanical Engineering The following table shows the kinetic energy and potential energy according to the speed of an object descending along a frictionless rain surface. What is the potential energy when the speed is 3/2v ? (It satisfies energy conservation) velocity kinetic energy 1500J potential energy V 3/2 * v 2v 1. 1400 J 2. 1000 J 3. 800 J 4. 600 J Please solve step by step. Thanks in advance! 1600 Jarrow_forwardWhat volume (in m3) of natural gas would it take to generate 5.94 x 108 J of energy if the energy content of natural gas is 36.9 MJ/m3 [round your final answer to one decimal place]?arrow_forward
- On an alien planet, the law that expresses the flow of blood through a blood vessel, F, as a function of the radius r of the vessel is f=kr5/2where k is a constant. Certain geological features of this planet produce a gas that changes the radius of blood vessels by 5% at the time of inhalation. What would the corresponding increase in blood flow through the vessel at this time be? Write 1-2 sentences explaining how you found your answer.arrow_forwardWhen an electrical appliance whose power usage is X watts is run for Y seconds, it uses X x Y joules of energy. The energy unit used by electrical utilities in their monthly bills is the kilo watt hour ( kwh, that is 1 kilowatt used for 1 hour ) how many joules are there in in a kilowatt hour ? If electricity cost $0.09 per kilo watt hour how much does it cost per megajoule?arrow_forwardWhat are the units of F in the equation below: F = mg/gc where m is mass in lbm; g is acceleration due to gravity 32.174 ft/s2 and gc is 32.174( lbm.ft)/ (lbf.s2). If m = 10 lbm what is F equal to in correct units?arrow_forward
- - 3 - Question 2A |Soalan 24] The spring is placed between the wall and 10-kg block. If the block is subjected to a force of F = 500N, (Spring diletakkan di antara dinding dan bongkah 10 kg. Jika bongkah itu dikenakan daya F = 50ON, Tentukan: (b) The work done by all the forces as the block moves 1.0m to the right with pulling force of 250N with an angle of 40°. Mass of the object is added with 6kg. Coefficient of friction is 0.50. Sketch together the free body diagram. [Kerja yang dilakukan oleh semua daya kerana blok bergerak Im ke kanan dengan daya tarikan 250N dengan sudut 40° Berat objek ditambah sebanyak ókg. Pekali geseran adalah 0.50. Lakarkan gambar rajah badan bebas.) 500 N k = 500 N/m wwww Figure 2 [Rajah 21arrow_forwardA company finds that if they price their product at $ 65, they can sell 690 items of it. For every dollar increase in the price, the number of items sold will decrease by 10. What is the maximum revenue possible in this situation? (Do not use commas when entering the answer) $ What price will guarantee the maximum revenue? $ Submit Question 國山品 12 MacBook Air esc 吕口 F3 F2 F4 F7arrow_forwardEngineering Mechanics IIA man shooting a ball to ring 19.68 ft high from the ground has a velocity of 16.2 m/s. If the angle made by the man is 38 degrees, determine the distance (in m) from where the man is shooting.you can download the book we are using through this link (it should help in getting the right answer) :https://drive.google.com/file/d/1Ws-HdkaO4OAfTMa1crhsf63rbClZUCl5/view?usp=sharingarrow_forward
- The following processes occurs in a reversible thermodynamic cycle: 1-2: Reversible polytropic compression at pressure [X] bar at volume [Y] m3 to a pressure [Z] bar and specific volume [A] m3/kg. The index of compression may be taken as n. 2-3: Reversibly expansion with expansion index of 2 to pressure [B] bar. 3-1: Reversible cooling at constant volume to the initial state. What are the final attempt values of X, Y, Z, A and B from the Part A of the eThuto Assessment. calculated formula similar question? X= ; Y= ; Z= ; A= ; B=arrow_forward1. Energy consumption in a country from 2001 to 2011 increased from 1041.3 million to 1526.1 million BOE (barrels of oil equivalent). If the high calorific value (HHV) of the oil is 141,000 kJ/gallon what is the increase in energy consumption over 10 years in Joule units. What is the rate of energy consumption per year? 2. Based on data on the rate of energy consumption per year from question no. 1, if the growth rate energy 2.5% per year, calculate the doubling time (td) and what is the approximate rate of energy growth in 2021.arrow_forwardYou plan to take a 1309-mile trip in your car, which averages 22 miles per gallon. How many gallons of gasoline should you expect to use? Would a car that has only half the gas mileage require twice as much gasoline for the same trip? Explain. gallons of gasoline. You should expect to use about (Type an integer or a decimal.)arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY