Chapter
6
Work
Done by a Variable Force
So
far we have used a constant force for our work calculations,
but we can also use a force that varies over time to calculate
work. To do this we need to use a little bit of calculus. For
a one-dimensional variable force we need to look at the Force
vs. Distance graph. We then have to find the area under the curve.
An estimate could be found using rectangles and adding them up
to find the area. The more rectangles the greater the accuracy.
But to get the exact answer you need to find the integral.
This
equation works for a one-dimensional variable force. If the force
is two or three dimensional you must add appropriate integrals.
Example
12
A
5.0 kg block moves in a straight line on a horizontal frictionless
surface under the influence of a force that varies with position
as shown in the figure. How much work is done by the force as
the block moves from the origin to x = 8.0 m?
Solution
Example
13
Force
,with x in meters, acts on a particle, changing only the kinetic
energy of the particle. How much work is done on the particle
as it moves from coordinates (2 m, 3 m) to (3 m, 0 m)? Does the
speed of the particle increase, decrease, or remain the same?
Solution
Example
14
What
work is done by a force ,with
x in meters, that moves a particle from a position to
a position ?
Solution
Potential Energy |