Chapter 6
Problem 75
†
Given
F = √bx = bx−1/2
Solution
Show that the work done going from x1 to x2 is finite even in the limit when x1 approaches zero.
Given the force function from this problem, it is clear that the force is undefined at x = 0. However, the
definition of work is
Z
W = F · dx
Putting in the force function and integrating between the given limits gives
Z x2
bx−1/2 dx
W =
x1
b is a constant so
1/2 x2
Z x2
x −1/2
W =b
x
dx = b
1/2 x1
x1
W =b
1/2
2x2
−
1/2
2x1
= 2b
1/2
x2
−
1/2
x1
As x1 approaches zero, the work done approaches
1/2
W = 2bx2
†
√
= 2b x2
Problem from Essential University Physics, Wolfson