1. 8-5 Applications from science

2. WORK
Work is force times displacement.
If the force is not constant, the work done is
Ex 1) Find the work done by the force F (x) = cos (x) newtons along the x-axis from x = 0 meters to x = ½ meters.

3. a) lifting the bucket alone
Ex 2) A leaky bucket weighs 22 newtons (N) empty. It is lifted from the ground at a constant rate to a point 20 m above the ground by a rope weighing 0.4 N/m. The bucket starts with 70 N (approx. 7.1 liters) of water, but it leaks at a constant rate and just finishes draining as the bucket reaches the top. Find the amount of work done
a) lifting the bucket alone
*weight constant (22 N)  (20 m) = 440 Nm = 440 J
b) lifting the water alone *weight is changing as it leaks
starting weight
proportion at height x

4. lifting the rope alone
*weight changes as it is pulled up
lifting the bucket, water and rope together
= 1220 J

5. Little slices / slabs from [0 , 8]
Ex 3) A conical tank (height is 10 ft, radius at the “bottom” is 5 ft) sitting on its apex is filled to within 2 ft of the top with olive oil weighing 57 lb/ft3. How much work does it take to pump the oil to the rim of the tank?
Note: r = ½h
Little slices / slabs from [0 , 8]
*the distance each slab/slice travels changes  (10 – y)
Sum them from 0 to 8

6. Area of base: Total force on base:
(This next example, is a bit of a sticky situation!) 
Ex 4) At 1:00 P.M. on January 15, 1919 (an unseasonably warm day), a 90-ft-high, 90-foot-diameter cylindrical metal tank in which the Puritan Distilling Company stored molasses at the corner of Foster and Commercial streets in Boston’s North End exploded! Molasses flooded the streets 30 feet deep, trapping pedestrians and horses, knocking down buildings, and oozing into homes. It was eventually tracked all over town and even made its way into the suburbs via trolley cars and people’s shoes. It took several weeks to clean up.
a) Given that the tank was full of molasses weighing 100 lb/ft3, what was the total force exerted by the molasses on the bottom of the tank at the time it ruptured?
Area of base:
Total force on base:

7. b) What was the total force against the bottom foot-wide band of the tank wall?
*the pressure is different at each spot between 89 & 90
each little band is y high & depth is yk
Force = pressure  area
wrap
2rh
Sum them

8. homework
Pg. 420 # 3, 9, 15
Pg. 429 # 1, 4, 5, 11, 13, 18