1. Section 8.5 Applications to Physics

2. International Units (SI)
In physics the word “work” is used to describe the work a force has done on an object to move it some distance
Work done = Force · Distance or W = F · D
Units
Force
Distance
Work
International Units (SI)
Newton (nt)
Meter (m)
Joule (j)
British Units
Pound (lb)
Foot (ft)
Foot-pound (ft-lb)

3. If an object of mass m moves along a straight line given by s(t), then the force (in the same direction) is defined by
What is the work required to raise a 5 kg mass up 10 meters?

4. What if the force is not constant?
Consider a force that varies along a to b
Call if f(x)
Divide the interval a to b into n subintervals
Pick in the ith interval
Then is the force
The interval is then small enough so that the force is constant
Then So

5. Hooke’s Law
The force required to maintain a spring stretched x units beyond its natural length is proportional to x (let k be the constant of proportionality) so we get
F = kx

6. Example
A spring has a natural length of 20 cm. If a 25 newton force is required to keep it stretched to 30 cm, how much work is required to stretch it from 20 cm to 25 cm?

7. Example
A trough that has a triangular cross section that is 5m high, 3m wide at the top and 8m long is filled up to 3 meters with water. Given that the density of water is 1000 kg/m3, how much work is required in order to empty the trough?

8. Force and Pressure
Can use a definite integral to compute the force exerted by a liquid on a surface
The force is directly related to the pressure
Pressure of a liquid is the force per unit area exerted by the liquid
It is equal in all directions
It increases with depth

9. At a depth of h meters, the pressure, p, exerted by the liquid is given by computing the total weight of a column of liquid h meters high with a base of 1 square meter.
If the liquid has density δ then its weight per unit volume is δg where g is the acceleration due to gravity. The weight of the column is δgh so Pressure = Mass density · g · Depth or P = δgh
Provided the pressure is constant over that area we have Force = Pressure · Area

10. International Units (SI)
Force
Area
Pressure
International Units (SI)
Newton (nt)
Meter2 (m2)
Nt/m2 called pascal
(mass)
British Units
Pound (lb)
Foot2 (ft2)
Lb/ft2
(weight)

11. Example
#24 The Three Gorges Dam is currently being built in China. When it is finished in 2009, it will be the largest damn in the world: about 2000 m long and 180 m high, creating a lake the length of Lake Superior. Assume the damn is rectangular in shape.
Estimate the water pressure at the base of the dam
Set up and evaluate a definite integral giving the total force of the water on the dam