A certain coiled spring with an unstretched length of 20cm required a force of 2N to stretch it by 0.2cm. What work is done in stretching it by 2cm if the elastic limit is not exceeded?
k = 2 N / .002 m = 1 kN / m
work = 1/2 k x^2 = (1/2) * (1 kN / m) * (.02 m)^2
answer is in Joules
Henry
yes , work does equal (force * distance)
the problem with a spring, is that the force is ALSO related to the distance
that's why the distance is squared in the spring work equation
Thanks for the explanation and information; I've used the Eq.(F*d) many times but never in this manner. Thanks!
To find the work done in stretching the spring by 2cm, we need to first find the spring constant (k) of the spring. The spring constant represents the stiffness of the spring and is a measure of the force required to stretch or compress the spring by a certain amount.
The spring constant can be calculated using Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement.
Hooke's Law can be written as:
F = k * x
Where F is the force applied, k is the spring constant, and x is the displacement.
We know that the spring requires a force of 2N to stretch it by 0.2cm. Let's use this information to find the spring constant:
2N = k * 0.2cm
First, we need to convert the displacement from centimeters (cm) to meters (m) to match the unit of force (Newtons).
0.2cm = 0.2/100 = 0.002m
Now we can rewrite the equation:
2N = k * 0.002m
Solving for k:
k = 2N / 0.002m
k = 1000 N/m
Now that we have the spring constant (k), we can find the work done in stretching the spring by 2cm.
The work done (W) in stretching a spring is given by:
W = (1/2) * k * x^2
Where W is the work done, k is the spring constant, and x is the displacement.
We want to find the work done in stretching the spring by 2cm:
x = 2cm = 2/100 = 0.02m
Substituting the values into the formula:
W = (1/2) * 1000 N/m * (0.02m)^2
W = (1/2) * 1000 N/m * 0.04m^2
W = 20 Joules
Therefore, the work done in stretching the spring by 2cm is 20 Joules.
F = 2N/0.2cm * 2cm = 10 N.
Work = F * d = 10 * 0.02 = 0.2 Joules.