If it requires 5.5 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additional 4.1 cm?
72N/m
To determine the additional work required to stretch the spring by an additional 4.1 cm, we can use Hooke's Law, which states that the force needed to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position.
Hooke's Law can be expressed as:
F = kx
Where:
F is the force applied to the spring,
k is the spring constant (a measure of how stiff the spring is), and
x is the displacement of the spring from its equilibrium position.
Given that it requires 5.5 J (joules) of work to stretch the spring by 2.0 cm, we need to first find the spring constant.
The work done on the spring can be calculated using the equation:
W = (1/2)kx^2
Where:
W is the work done on the spring.
Rearranging the equation, we have:
k = (2W)/(x^2)
Substituting the given values, we can calculate the spring constant:
k = (2 * 5.5 J) / (0.02 m)^2
k ≈ 2750 N/m
Now that we know the spring constant, we can calculate the additional work required to stretch the spring by an additional 4.1 cm.
We need to find the force (F) required to stretch the spring by 4.1 cm:
F = kx
F = (2750 N/m)(0.041 m)
F ≈ 112.75 N
The work done to stretch the spring by an additional 4.1 cm can be calculated using the equation:
W = (1/2)kx^2
W = (1/2)(2750 N/m)(0.041 m)^2
W ≈ 2.63 J
Therefore, approximately 2.63 J of additional work will be required to stretch the spring by an additional 4.1 cm.