1. Section 6.4 Work

2. 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 UnitsForceDistanceWork InternationalNewton (N)Meter (m)Joule (j) BritishPound (lb)Foot (ft)Foot-pound (ft-lb)  Lifting object vertically:  Example: What is the work done in lifting 120 pound object 4 feet off the ground? Work

3.  If a force F(x) varies along a to b, then the work done by the force as the object is moved from a to b is:  Hooke’s Law: The force required to maintain a spring stretched x units beyond its natural length is proportional to x: F = k x where k is called the spring constant http://www.intmath.com/applications-integration/7- work-variable-force.php Variable Force

4. A spring has a natural length of 1 m. A force of 24 N stretches the spring to 1.8 m. a Find k : b How much work would be needed to stretch the spring 3m beyond its natural length? Example

5. A 5 lb bucket is raised 20 feet. How much work is done if the rope weighs 0.08 lb/ft? Work: Bucket: Rope: Check: Total: Example

6. 5 ft 10 ft 4 ft 5 ft 10 ft 10 0 4 ft dy I want to pump the water out of this tank. How much work is done? (Water weighs 62.5 lb per cubic foot) Consider the work to move one “slab” of water: Example

7. 10 ft 5 ft 10 ft 10 0 4 ft dx A 1 horsepower pump, rated at 550 ft-lb/sec, could empty the tank in just under 14 minutes! forcedistance 5 ft 10 ft 4 ft

8. 10 ft 2 ft 10 ft A conical tank is filled to within 2 ft of the top with salad oil weighing 57 lb/ft 3. How much work is required to pump the oil to the rim? Consider one slice (slab) first: Example

9. 10 ft 2 ft 10 ft

10. 1)A spring has a natural length of 20 cm. If a 25 N force is required to keep it stretched to 30 cm, how much work is required to stretch it from 20 cm to 25 cm? 2)A tank full of water has a triangular cross section that is 5m high, 3m wide at the top and 8m long. Given that the density of water is 9800 N/m 3, how much work is required in order to empty the tank? Examples