Phys205A_Lecture17

# Physics for Scientists & Engineers with Modern Physics (4th Edition)

This preview shows pages 1–12. Sign up to view the full content.

Chapter 7 Kinetic and Potential Energy of a System Lecture 17-18

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Work Done by a Varying Force z Assume that during a very small displacement, x , F is constant z For that displacement, W ~ F x z For all of the intervals, ≈∆ f i x x x WF x X F F x W = F D x cos a What if F changes the value and/or direction?
Work Done by a Varying Force, cont z z Therefore, z The work done is equal to the area under the curve between x i and x f ∆→ ∆= lim 0 f f i i x x xx x x x Fx F d x = f i x x x WF d x Eample:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Work Done By Multiple Forces z If more than one force acts on a system and the system can be modeled as a particle , the total work done on the system is the work done by the net force () == ∑∑ f i x net x x WW F d x
Work Done by Multiple Forces, cont. z In the general case of a net force whose magnitude and direction may vary z If the system cannot be modeled as a particle, then the total work is equal to the algebraic sum of the work done by the individual forces z Remember work is a scalar, so this is the algebraic sum = net by individual forces WW () == ∑∑ Fr r r f i x net x d m1 m2 m3 L1 L2 W-?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example of varying force: Work Done By A Spring z A model of a common physical system for which the force varies with position z The block is on a horizontal, frictionless surface z The force exerted by the spring is always directed opposite to the displacement from equilibrium z The spring force is sometimes called the restoring force z If the block is released it will oscillate back and forth between – x and x
Hooke’s Law z The force exerted by the spring is F s = - kx z x is the position of the block with respect to the equilibrium position ( x = 0) z k is called the spring constant or force constant and measures the stiffness of the spring z This is called Hooke’s Law

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Hooke’s Law, cont. z When x is positive (spring is stretched), F is negative z When x is 0 (at the equilibrium position), F is 0 z When x is negative (spring is compressed), F is positive
Work Done by a Spring z Identify the block as the system z Calculate the work as the block moves from x i = - x max to x f = 0 z Interestingly: The total work done as the block moves from x max to x max is zero () == = ∫∫ max 0 2 1 2 f i x sx xx W F dx kx dx kx

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Work Done by a Spring, cont. z Assume the block undergoes an arbitrary displacement from x = x i to x = x f z The work done by the spring on the block is z If the motion ends where it begins, W = 0 () =− = 22 11 f i x si f x Wk x d x k x k x
Spring with an Applied Force z Suppose an external agent, F app , stretches the spring z The applied force is equal and opposite to the spring

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This document was uploaded on 09/27/2011.

### Page1 / 40

Phys205A_Lecture17 - Lecture 17-18 Chapter 7 Kinetic and...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online