Question: The potential function associated with a force P in space is known to be V(x,y,z) = -(x2 + y2 + z2)1/2. (a) Determine the x,

The potential function associated with a force P in space is known to be

V(x,y,z) = -(x2 + y2 + z2)1/2.

(a) Determine the x, y, and z components of P.
(b) Calculate the work done by P from O to D by integrating along the path OABD, and show that it is equal to the negative of the change in potential from O to D.

D. B.

Step by Step Solution

★★★★★

3.48 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a b U OABD U OA U AB U BD O A P y and P x are perpendi... 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)

1221-P-M-K(2414).docx

120 KBs Word File

Students Have Also Explored These Related Mechanics Questions!

(a) Calculate the work done from D to O by the force P of Problem 13.82 by integrating along the diagonal of the cube. (b) Using the result obtained and the answer to part b of Problem 13.82, verify...

The force F = (yzi + zxj + xyk)/ xyz acts on the particle P(x,y,z) which moves in space. (a) Using the relation derived in Prob. 13.77, show that this force is a conservative force. (b) Determine the...

Figure 7.22b shows the potential energy function associated with the gravitational force between an object and the earth. Use this graph to explain why objects always fall toward the earth when they...

878 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES (e) Does P correspond to a minimum or maximum value of f? Re- fer to Figure 12 to justify your answer. Hint: Do the values of f(x, y) 2 increase or...

1 Multivariable functions and vector geometry Due date and time: Wednesday, June 7th at 9:30 AM in lecture Please ensure that you have read and understood the document \"Homework Guidelines" on the...

854 CHAPTER 15 DIFFERENTIATION IN SEVERAL VARIABLES 9. 20. Jessica and I at 2 oh ; h (x , y ) = -, x = 1/2, y = 1712 paths that make a with velocity va 10. "J : f ( x , y , Z ) = xy - 22, x = rcos0,...

\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...

SECTION 15.5 24. f (x, y) = sin(x - y), v= (1,1), P = (5, 6) 45. Use the geostrophi 25. f (x, y ) = tan-1 (xy), v = (1,1), P = (3,4) ern Hemisphere, winds together the isobars, 26. f (x, y ) = exy...

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

How many states belong to each of the following carbon configurations? (a) 1s22s22p2; (b) 1s22s22p3P.

Matthison Harcourt plans to issue $550,000 face value bonds with a stated interest rate of 8%. They will mature in 5 years. Interest will be paid semiannually. At the date of issuance, assume that...

Discuss why Capital Budgeting is imperative to growth for an organization.

Discuss the role and advantages of centralized distribution system and tiering of suppliers at McDonalds.

Two 12-lb uniform disks are attached to the 20-lb rod AB as shown. Knowing that the constant of the spring is 30 lb/in. and that the disks roll without sliding, determine the frequency of vibration...

A 15-lb uniform cylinder can roll without sliding on an incline and is attached to a spring AB as shown. If the center of the cylinder is moved 0.4 in. down the incline and released, determine (a)...

The crude-oil pumping rig shown is driven at 20 rpm. The inside diameter of the well pipe is 2 in., and the diameter of the pump rod is 0.75 in. The length of the pump rod and the length of the...

Problem 2-10 Cash Flow to Stockholders [LO 4] The December 31, 2021, balance sheet of Chen, Incorporated, showed $139,000 in the common stock account and $2,640,000 in the additional paidin surplus...

A production company not so long ago paid a dividend of $2.50 per share and plans to increase its dividends by 10% in the first year, 15% in year 2, 20% in year 3 then at a constant rate of 5%...

Time Value Of Money - Present Value of Growing Annuity Hi, Could You Apply This Formula: Present Value of Growing Annuity = Cashflow / Interest Rate Growth Rate [ 1-(1+Growth Rate /1+ Interest...