Work
If an object is moved a distance d using a constant force, (Force)(distance). The units are either foot-pounds (ft-lb) or Newton meters = joules. Work is only done when moving the object.
Ex. How much work is done by a weightlifter in raising a 60 kg barbell from the floor a height of 2 meters?
Suppose we use a variable force, F(x), which depends on position.
Total work = W =
Springs:
Hooke’s Law: F(x) = kx
The force necessary to keep a spring stretched or compressed x units beyond (or short of) its natural length is proportional to x.
Ex. A force of 8 lb. Is required to keep a spring compressed 1/2 ft. below its normal length. Find k and the work done.
Ex. A spring has a natural length of .5 m. A force of 50N stretches the spring to a length of .6 m.
a. What force is needed to stretch the spring x m ?
b. How long is the spring when stretched by a force of 200 N?
c. Find the work done in stretching the spring .2 m.
d. Find the work done in stretching the spring from a length of 1 m. to 1.1 m.
e. 20 J of work is done in stretching the spring a certain distance. How far was the spring stretched?
Do: a. If 6 J of work is required to stretch a spring with a natural length of 8 cm from 10 cm to 12 cm, what force is required to stretch it to 12 cm?
b. How far beyond its natural length will a force of 100 N stretch the spring?
Pulley systems
Ex. A uniform cable 30 ft long and weighing 60 lb. Hangs vertically from a pulley system at the top of a building. A steel beam weighs 500 lbs. And is attached to the end of the cable.
a. Find the work required to pull it to the top.
b. Find the work required to pull it up 10 ft.
Ex. (From Fall 2005) A flat metal plate weighing 100 lbs is being pulled up the side of a 50 foot building by a rope weighing ½ pound per linear foot. As it is pulled up the excess rope is dropped on the top of the building. How much work (in foot pounds) is done in raising the plate from ground level to a point 20 feet above the ground?
(1) (125)(20) (2) (100)(20)
(3) (4)