1. Section 6.4.1 Work AP Calculus May 19, 2010 Berkley High School, D1B1

2. Calculus, Section 6.4, Todd Fadoir, CASA, 20042 First, “Force” in SI Mass (m) is measured  kilograms the remainder is the second derivative of position  acceleration measured in m/s 2 Force (F) is measured in  Newtons (N)

3. Calculus, Section 6.4, Todd Fadoir, CASA, 20043 Second, “Force” in English Is measured in…  pounds (lbs)

4. Calculus, Section 6.4, Todd Fadoir, CASA, 20044 Third, “Work” in SI Force (F) is measured in  Newtons (N) Distance (d) is measured in  meters (m) Work is measured in  Joules (J)

5. Calculus, Section 6.4, Todd Fadoir, CASA, 20045 Fourth, “Work” in English Force (F) is measured in  pounds (lb) Distance (d) is measured in  feet (ft) Work is measured in  ft-lbs

6. Calculus, Section 6.4, Todd Fadoir, CASA, 20046 Example: How much work is done in lifting a 1.2 kg book off the floor to put it on a desk that is.7 m high? Remember that acceleration due to gravity is 9.8 m/s 2.

7. Calculus, Section 6.4, Todd Fadoir, CASA, 20047 Example: How much work is done in lifting a.54 lb book off the floor to put it on a desk that is 2.3 ft high?

8. Calculus, Section 6.4, Todd Fadoir, CASA, 20048 Example: When a particle is located at a distance x feet from the origin, a force of x 2 +2x pounds acts on it. How much work is done in moving it from x=1 to x=3?

9. Calculus, Section 6.4, Todd Fadoir, CASA, 20049 Hooke’s Law (work done on and by springs) Hooke’s Law is concerned with the amount of force needed to hold a spring away from its natural length The law states that the force varies directly to the displacement from natural position. For example, at natural length, it requires no force. It requires twice as much force to hold a spring two meters from natural length as it does to hold it 1 meter.

10. Calculus, Section 6.4, Todd Fadoir, CASA, 200410 Hooke’s Law (SI) F=kx where… F is force measured in…  Newtons (N) x is the displacement of the length of the spring from its natural length measured in…  meters (m) k is the spring constant (which varies from spring to spring) measured in…  kilograms per seconds 2 (kg/s 2)

11. Calculus, Section 6.4, Todd Fadoir, CASA, 200411 Hooke’s Law (English) F=kx where… F is force measured in…  pounds (lbs) x is the displacement of the length of the spring from its natural length measured in…  feet (ft) k is the spring constant (which varies from spring to spring) measured in…  pounds per foot (lbs/ft)

12. Calculus, Section 6.4, Todd Fadoir, CASA, 200412 Example: A spring requires 20 Newtons of force to hold it at 15 cm. Its natural length is 10 cm. How much work is done in pulling it from 15 cm to 20 cm?

13. Calculus, Section 6.4, Todd Fadoir, CASA, 200413 Example: A spring requires 15 Joules of work to move it from 20 cm to 25. Its natural length is 10 cm. How much work is done in pulling it from 15 cm to 20 cm?

14. Calculus, Section 6.4, Todd Fadoir, CASA, 200414 Example: A spring requires 15 Joules of force to move it from 20 cm to 25. Its natural length is 10 cm. How much work is done in pulling it from 15 cm to 20 cm?

15. Calculus, Section 6.4, Todd Fadoir, CASA, 200415 Assignment Section 6.4, 1-10 all