If it requires 5.5J of work to stretch a particular spring by 2.3cm from its equilibrium length, how much more work will be required to stretch it an additional 4.5cm ?
Express your answer using two significant figures.
W=_____ J?
To solve this problem, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position.
The equation for Hooke's Law is:
F = kx
Where F is the force applied to the spring, k is the spring constant, and x is the displacement from the equilibrium position.
Since work (W) is defined as the product of force and displacement, we can calculate the work done on the spring using the equation:
W = F * x
To find the work required to stretch the spring an additional 4.5 cm, we need to calculate the force required for that displacement and then multiply it by the displacement.
First, let's calculate the force required to stretch the spring by 2.3 cm using the given work of 5.5 J.
W = F * x
5.5 J = F * 0.023 m
Rearranging the equation, we get:
F = 5.5 J / 0.023 m
F ≈ 239 J/m
Now, we can use this force to calculate the work required to stretch the spring an additional 4.5 cm.
W = F * x
W = 239 J/m * 0.045 m
Calculating this, we find:
W ≈ 10.8 J
Therefore, the additional work required to stretch the spring an additional 4.5 cm is approximately 10.8 J.