1. Work
Lesson 7.5

2. Work Definition The product of
The force exerted on an object
The distance the object is moved by the force
When a force of 50 lbs is exerted to move an object 12 ft.
600 ft. lbs. of work is done 50
12 ft

3. Hooke's Law Consider the work done to stretch a spring
Force required is proportional to distance
When k is constant of proportionality
Force to move dist x = k • x = F(x)
Force required to move through i th interval, x
W = F(xi) x a b x

4. Hooke's Law We sum those values using the definite integral
The work done by a continuous force F(x)
Directed along the x-axis
From x = a to x = b

5. Hooke's Law A spring is stretched 15 cm by a force of 4.5 N
How much work is needed to stretch the spring 50 cm?
What is F(x) the force function?
Work done?

6. Winding Cable Consider a cable being wound up by a winch
Cable is 50 ft long
2 lb/ft
How much work to wind in 20 ft?
Think about winding in y amt
y units from the top  50 – y ft hanging
dist = y
force required (weight) =2(50 – y)

7. Pumping Liquids
Consider the work needed to pump a liquid into or out of a tank
Basic concept: Work = weight x dist moved
For each V of liquid
Determine weight
Determine dist moved
Take summation (integral)

8. Pumping Liquids – Guidelinesa b r
Draw a picture with the coordinate system
Determine mass of thin horizontal slab of liquid
Find expression for work needed to lift this slab to its destination
Integrate expression from bottom of liquid to the top

9. Pumping Liquids Suppose tank has
r = 4
height = 8
filled with petroleum (54.8 lb/ft3)
What is work done to pump oil over top
Disk weight?
Distance moved?
Integral? 4 8
(8 – y)

10. Work Done by Expanding Gas
Consider a piston of radius r in a cylindrical casing as shown here
Let p = pressure in lbs/ft2
Let V = volume of gas in ft3
Then the work increment involved in moving the piston Δx feet is

11. Work Done by Expanding Gas
So the total work done is the summation of all those increments as the gas expands from V0 to V1
Pressure is inversely proportional to volume so p = k/V and

12. Work Done by Expanding Gas
A quantity of gas with initial volume of 1 cubic foot and a pressure of 2500 lbs/ft2 expands to a volume of 3 cubit feet.
How much work was done?

13. Moving Space Module to Orbit
Consider a rocket which weighs 2 tons on the moon.
The moon has a radius of 1100 miles
How much work is required to propel the rocket to an altitude of 50 miles above the moon?

14. Moving Space Module to Orbit
Weight of a body varies inversely as square of distance from center of a planet or moon
Recall radius of moon = 1100 mi.
Use weight = F(x) and radius = x to determine constant C
Now integrate F(x) over range of x

15. Assignment
Lesson 7.5
Page 405
Exercises 1 – 41 EOO