Question: General Proof of the Work-Energy Theorem Consider a particle that moves along a curved path in space from (x1, y1, z1) to (X2, Y2,Z2) At

General Proof of the Work-Energy Theorem Consider a particle that moves along a curved path in space from (x1, y1, z1) to (X2, Y2,Z2) At the initial point, the particle bas velocity it = v,i + v,, + vi. The path that the particle follow~ may be divided into infinitesimal segments d1 = dxi + djj + dzk. As the particle moves, it is acted on by a net force F = Fxi; + Fyj + Fzk. The force components F .. Fy , and F, are in general functions of position. By the same sequence of steps used in Eqs (6.11) through (6.13), prove the work-energy theorem for this general case. That is, prove that

General Proof of the Work-Energy

where K-Ihnalp.a-(F.ds + r,dy + tot

Step by Step Solution

★★★★★

3.54 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

IDENTIFY Write equations similar to 611 for each component Eq612 will now involve the sum of ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

P-M-W-E (103).docx

120 KBs Word File

Students Have Also Explored These Related Mechanics Questions!

A particle with mass m is acted on by a conservative force and moves along a path given by x = xo cos w0t and y = yosinwot, where x, yo, and wo are constants. (a) Find the components of the force...

A particle that moves along a straight line has velocity v(t) = t2 et meters per second after seconds. How far will it travel during the first seconds?

A particle that moves along a straight line has velocity v(t) = t2e-t meters per second after seconds. How far will it travel during the first seconds?

Digital Communication I X A B C D Y Hosts X and Y are communicating through the data network provided by the switches A, B, C and D and the links interconnecting them as shown above. Initially all...

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

Predictive text entry systems are familiar on touch screens and mobile phones. This question asks you to consider how the same principles might be used in a programming editor for creating Java code....

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Chapter Thirteen A FUNDAMENTAL TOOL: VECTORS Contents 13.1 Displacement Vectors . . . . . . . . . . . . 686 Notation and Terminology . . . . . . 686 Addition and Subtraction of Displacement Vectors ....

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

f a processor exhibited one branch delay slot how would you reorder (and possibly modify) the instructions in the following loop to gain a performance advantage? loop ldr r2,r3,#4 % r2=load(r3),...

Assume that the current 6-month futures price of coffee is 23 SEK per kilo with an annual volatility of 42%. If the annual risk-free rate of interest is 3.25%, calculate the delta of a short position...

Eva Designs, Inc., a corporation organized on January 1, 2005, reported the following incomes (losses) for the ten-year period, 2005-2014: Year Income (Loss) Income Tax Rate Income Tax Paid 2005...

for the function f ( x ) = - 4 x ^ 2 + 4 x - 3 , find the difference quotient ( f ( x + h ) - f ( x ) ) / h , given that h does not equal 0 in the simplest form

There are four elements that can be discussed to understand the major differences between perfect competition and monopoly; namely, price, output, profit and efficiency (productive and allocative)....

Figure 6 QUESTION No. 6: i -- (5 POINTS) Two semicircular uniform nonconducting loops, each of radius R, are charged oppositely to +Q and -Q, respectively. The loops are now joined end to end to form...

for the given cct 6 kn 6 kn (1) 6 kn 12 u(t) v va(t) 2 mA 6 k2 50 uF the voltage Vc (t = taw) is:* (1 Point)

Review the example in the three parts of the Management Close-Up. What other organizations or industries have faced or are facing similar circumstances in their external environments?

The following option prices were observed for a stock for July 6 of a particular year. Ignore dividends on the stock. The stock is priced at 165.13. The expirations are July 17th, August 21, and...

For the given cash flows, suppose the firm uses the NPV decision rule. Year Cash Flow 158,000 0 1 2 3 58,000 81,000 65,000 a. At a required return of 9 percent, what is the NPV of the project? (Do...

HW_08 Consider the applications for home mortgages data in the file of P12_04.xlsx. Create a time series chart of the data. Use simple exponential smoothing to forecast these data, using the default...