A spring has a natural length of 25 meters. A force of 12 newtons is required to stretch the spring to a length of 30 meters. How much work is done to stretch the spring from it's natural length to 40 meters?
-I forgot to add the 40 meters part to my other question
here is what i have done and i cant figure out what to do:
F = ks
12 = k(15)
12/15 = k
integrating from 0 to 15
12/15 sds
12/15 x S squared / 2 from 0 to 15
i end up with 225/2. the answer is supposed to be 270 and i dont understand why i cant do this, please help. thank you
To find the work done to stretch the spring from its natural length to 40 meters, you need to calculate the area under the force-distance graph. Since the force required to stretch the spring is not given for 40 meters, you will need to use Hooke's Law equation to find the spring constant (k) first.
We know that F = ks, where F is the force required, k is the spring constant, and s is the change in length. Given that the force required to stretch the spring to 30 meters is 12 newtons, we can substitute these values into the equation:
12 = k(30 - 25)
12 = 5k
k = 12/5
k = 2.4 N/m
Now that we have the spring constant, we can calculate the work done to stretch the spring from its natural length to 40 meters. The formula for work is W = (1/2)kx^2, where W is the work done, k is the spring constant, and x is the displacement.
First, let's find the work done to stretch the spring from 25 meters to 30 meters:
W1 = (1/2)(2.4)(30 - 25)^2
W1 = (1/2)(2.4)(5)^2
W1 = (1/2)(2.4)(25)
W1 = 30 joules
Now, let's find the work done to stretch the spring from 30 meters to 40 meters:
W2 = (1/2)(2.4)(40 - 30)^2
W2 = (1/2)(2.4)(10)^2
W2 = (1/2)(2.4)(100)
W2 = 120 joules
Therefore, the total work done to stretch the spring from its natural length to 40 meters is the sum of W1 and W2:
Total work = W1 + W2
Total work = 30 + 120
Total work = 150 + 120
Total work = 270 joules
So, the correct answer is indeed 270 joules, not 225/2 as you calculated.