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Chapter 6: Q3P (page 284)

Find the total work done by forces and if the object undergoes the displacement C . Hint: Can you add the two forces first?

Short Answer

Expert verified

The required work done is, W=‐5.

Step by step solution

01

Definition of work done

By substituting the force with the equation of

W=F.dW=F.d

Where Fis the force andd is the displacement andW is equal to the work.

02

Simplify

Let us know if work done can be calculated as,

W=F.d

To find F

role="math" localid="1659153886346" F=A+B,d=C

Substitute the values in the equation

W=A+B×C=i+j-2k+2i-j+3k×j-5k=3i+k+j-5k=-5

Therefore, the work done is W=‐5

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Most popular questions from this chapter

Do case (b) of Example 1above.

If the temperature is T=x2-xy+z2, find

(a) The direction of heat flow at (2,1, -1);

(b) The rate of change of temperature in the direction j-kat(2,1,-1)

Let F = 2i - 3j + k act at the point (5, 1, 3)

(a) Find the torque of F about the point (4, 1, 0)

(b) Find the torque of F about the line r = 4i + j + (2i + j - 2k)t.

The force F = i - 2jacts at the point (0, 1, 2) Find the torque of F about the line =(2i-j)t.

Given

F1=-2yi+(z-2x)j+(y+z)kF2=yi+2xj:

(a) Is F1conservative? Is F2conservative?

(b) Find the work done by 2 on a particle that moves around the ellipse x=cosθ, y=2sinθfrom θ=0toθ=2π

(c) For any conservative force in this problem find a potential function Vsuch

that F=-∇V (d) Find the work done by on a particle that moves along the straight line from (0,1,0)to(0,2,5)

(e) Use Green’s theorem and the result of Problem 9.7 to do Part (b) above.
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