Q34E An object moving in the xy-plane... [FREE SOLUTION]

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University Physics with Modern Physics

Hugh D. Young, Roger A. Freedman

Physics

14th edition Edition 路 1596 pages

ISBN: 9780321973610

Chapter 1: Q34E (page 230)

An object moving in the xy-plane is acted on by a conservative force described by the potential-energy function $U (x, y) = 伪 [(1 / x^{2}) + (1 / y^{2})]$ , where is a positive constant. Derive an expression for the force expressed in terms of the unit vectors role="math" localid="1665045813739" $\hat{i}$ and $\hat{j}$ .

Short Answer

Expert verified

The expression for the force on an object in terms of unit vectors is $2 伪 (\frac{1}{x^{3}} \hat{i} + \frac{1}{y^{3}} \hat{j})$ .

Step by step solution

Given Data:

The potential energy of the particle is $U (x, y) = 伪 [(1 / x^{2}) + (1 / y^{2})]$

Force:

The force on the object in the above problem is calculated by derivating the potential energy function of the object.

Determination of formula for force on an object

The magnitude of the force is given as:

$\overset{鈫�}{F} = - (\frac{dU}{dx} \hat{i} + \frac{dU}{dy} \hat{j})$

$\overset{鈫�}{F}$ is the force on the object

Determination of the expression for the force on the object

Substitute all the values in the above equation.

$\overset{鈫�}{F} = - (\frac{d}{d x} (伪 [(1 / x^{2}) + (1 / y^{2})]) \hat{i} + \frac{d}{d y} (伪 [(1 / x^{2}) + (1 / y^{2})]) \hat{j}) \overset{鈫�}{F} = - [(\frac{- 2 伪}{x^{3}}) \hat{i} + (\frac{- 2 伪}{y^{3}}) \hat{j}] \overset{鈫�}{F} = 2 伪 (\frac{1}{x^{3}}) \hat{i} + (\frac{1}{y^{3}}) \hat{j}$

Therefore, the expression for the force on an object in terms of unit vectors is $2 伪 (\frac{1}{x^{3}}) \hat{i} + (\frac{1}{y^{3}}) \hat{j}$ .

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Short Answer

Step by step solution

Given Data:

Force:

Determination of formula for force on an object

Determination of the expression for the force on the object

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91影视

An object moving in the xy-plane is acted on by a conservative force described by the potential-energy function U(x,y)=伪[(1/x2)+(1/y2)], where is a positive constant. Derive an expression for the force expressed in terms of the unit vectors role="math" localid="1665045813739" i^ and j^.

Short Answer

Step by step solution

Given Data:

Force:

Determination of formula for force on an object

Determination of the expression for the force on the object

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Engineering Physics

Fields in Physics

Medical Physics

Electrostatics

Radiation

Study anywhere. Anytime. Across all devices.