Work & Energy 03

OPENING QUESTIONS:

  1. List the 3 main equations for calculating horizontal motion in less than 30 seconds
  2. What the units of measure for work?
  3. Define work (in physixy terms)
  4. What units themselves comprise the unit of measure for work?
  5. Calculate the "dot" product of -4i - 6j with -2i + 6j
  6. Calculate the angle made between those two vectors.
  7. Be prepared to explain why we DO NOT treat the i and j UNIT VECTORS as algebraic terms per se...
  8. Be prepared to lead a conversation as to why a "dot" product is a scalar quantity... especially in light of the fact that both starting quantities are vectors

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LEARNING OBJECTIVES:

I will develop a working knowledge of a 'restorative' force during today's class.

I will be able to relate work to the change of position of a spring during today's class.

WORDS O' THE DAY:

  • Work (Force through displacement)
  • Dot Product ("scalar product")
  • Work ("Newton meter (Nm)" or "Joule (J) ")
  • RESTORATIVE force (results in acceleration in the opposite direction of the applied force)

FORMULAE OBJECTUS:

  • Work = fdcosθ (including the integral form)
  • F = -kx (note the negative sign)
  • Work done by a spring = 1/2kx2
  • Kinetic Energy of an object = 1/2mv2

WORK O' THE DAY:

Let's take a look at a slinky....

BACK TO WORK (so to speak)

A very important concept in work/energy involves the work done on or by a spring:

asdf

 

the force either exerted on a spring (to compress it) or by the spring on an object as it decompresses is given by the equation:

Fs = -kx

(This is Hooke's Law, btw)

Where x is the displacement by the spring as it returns to equilibrium

Or

x is the displacement the spring experiences as it is compressed

and k is the spring constant of that particular type of spring.

Notice the '-' sign...

Why is that present?

What are the UNITS of the spring constant (careful!)?

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HOMEWORK:

  • Do problems 5 (read this one CAREFULLY) on page 203

  • Problems 19 & 24 (look at your force values CAREFULLY esp in part b), 26 (ADDITIONALLY, also please use calculus to solve this problem...why?