The strength of magnetic force varies inversely with the square of the distance between the magnets. In other words,
Force= k/distance^2
Suppose that k=0.0064. Find the work required to move the magnets from a distance of 0.03m apart to a distance of 0.09 m apart.
Work = (0.0064/0.09^2) - (0.0064/0.03^2) = 0.0064/0.0081 = 0.79 mJ
AAAaannndd the bot gets it wrong yet again!
since the force is not constant, the simple work=Fd does not work.
Also, (0.0064/0.09^2) - (0.0064/0.03^2) = -6.32
The work is
∫[0.3,0.9] 0.0064/r^2 dr = 0.0142
Huh? That is the difference in forces.
F = k/x^2
work = integral F dx
= k * integral from x = .03 to x = .09 of 1/x^2
= -k ( 1/.09 - 1/.03)
= - k (11.1 - 33.3) = 22.2 k = 22.2 * 0064 = .142 Joules
note integral (dx/x^2) = -1/x
To find the work required to move the magnets from a distance of 0.03m apart to a distance of 0.09m apart, we need to use the formula for work.
Work (W) is defined as the force (F) applied over a distance (d), so we have:
W = F * d
Given that the force (F) varies inversely with the square of the distance (d), we can rewrite the equation as:
F = k / distance^2
where k = 0.0064.
Now, we need to determine the initial force and the final force.
Initial force (F1) when the magnets are 0.03m apart:
F1 = k / (0.03)^2
Final force (F2) when the magnets are 0.09m apart:
F2 = k / (0.09)^2
Next, we can find the work required by subtracting the initial force from the final force, and then multiplying that difference by the distance over which the magnets were moved:
W = (F2 - F1) * (0.09 - 0.03)
Substituting the values of F1, F2, and k, we can calculate the work:
W = (k / (0.09)^2 - k / (0.03)^2) * (0.09 - 0.03)
W = (0.0064 / (0.09)^2 - 0.0064 / (0.03)^2) * (0.09 - 0.03)
Calculating the values inside the parentheses:
W = (0.0064 / 0.0081 - 0.0064 / 0.0009) * 0.06
W = (0.79012 - 7.11111) * 0.06
Calculating the difference and multiplying by 0.06:
W = (-6.32099) * 0.06
W = -0.37926
Therefore, the work required to move the magnets from a distance of 0.03m apart to a distance of 0.09m apart is approximately -0.37926 Joules.