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

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Presentation transcript:

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

Calculus, Section 6.4, Todd Fadoir, CASA, 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)

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

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

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

Calculus, Section 6.4, Todd Fadoir, CASA, 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.

Calculus, Section 6.4, Todd Fadoir, CASA, 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?

Calculus, Section 6.4, Todd Fadoir, CASA, 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?

Calculus, Section 6.4, Todd Fadoir, CASA, 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.

Calculus, Section 6.4, Todd Fadoir, CASA, 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)

Calculus, Section 6.4, Todd Fadoir, CASA, 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)

Calculus, Section 6.4, Todd Fadoir, CASA, 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?

Calculus, Section 6.4, Todd Fadoir, CASA, 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?

Calculus, Section 6.4, Todd Fadoir, CASA, 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?

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