A can of sardines is made to move along an x axis from x1 = 0.2 m to x2 = 1.2 m by a force given by F = iF0exp(-0.4x), with x in meters and F0 = 4.5 N. (Here exp is the exponential function.) How much work is done on the can by the force?
Work is the integral of force x distance.
In this case,
------1.2
W = (Integral)4.5 exp(-0.4x)dx
------0.2
= 4.5/(-0.4)[exp(-0.4*1.2) - exp(-0.4*0.2)]
Ok thanks...I will try that :)
You're welcome! Just to clarify, the work done on the can by the force is given by the integral of the force function over the distance the can moves. So we need to evaluate the integral of 4.5 * exp(-0.4x) with respect to x from x = 0.2 to 1.2.
To calculate the integral, we can use the anti-derivative of the exponential function. The anti-derivative of exp(-0.4x) with respect to x is -(1/0.4) * exp(-0.4x).
Therefore, the work done on the can can be calculated as follows:
W = [-(1/0.4) * 4.5 * exp(-0.4x)] evaluated from x = 0.2 to 1.2
Substituting the values:
W = [-(1/0.4) * 4.5 * exp(-0.4*1.2)] - [-(1/0.4) * 4.5 * exp(-0.4*0.2)]
Now you can calculate the value and find the work done on the can by the force!