Work Part 1

1. Quiz
   

2. Homework
   

3. Work
   We define the work, W,  done in moving an object a distance s units with a force of F as:

   W = Fs

   Example:  For me to jump 2 feet in the air, if I weigh 165 pounds takes

   W = Fs = 165(2) = 330 foot pounds.
   

4. Hook's Law
   For a spring
   

   F = kd

   where d is the distance the spring is from its equilibrium point.

   Example:  To compress a spring 2 inches from its equilibrium point requires 50 pounds of force.  How much work is it to compress the spring an additional 2 inches?

   Solution:  We first find k:

   50 = k(2)  hence k = 25.

   We have F = 25d.  To find the work done, we cut the work into small intervals of work.  The force required to move the spring Dx units is 25x, hence the work required is 25x Dx
   Adding the small intervals, we have that

   
   

5. Rockets

   Example:  Sending a rocket to mars:
   Suppose that a 50 ton rocket is to be sent to mars and after 100,000 miles, the rocket is completely free of the earths gravity.  If the radius of the earth is 4,000 miles, how much work is required to send the rocket out of orbit?

   Solution:  We use that the force of gravity is inversely proportional to the square of the distance from the center of the earth.  
   

   F = k/x2

   We have that 50 tons = k/(4000)²  or that k = 800,000,000.

   We have that the work = Fs cutting the work into small intervals and adding, we have