If a certain spring stretches 9.76811 cm when a load of 17.9936 N is suspended from it, how much will the spring stretch if it is cut in half and 65.8458 N is suspended from it?
Answer in units of cm.
To solve this problem, we can use Hooke's Law, which states that the amount of stretch or compression in a spring is directly proportional to the force applied to it.
Hooke's Law can be written as:
F = k * x
Where:
F is the force applied to the spring,
k is the spring constant, and
x is the amount of stretch or compression.
Let's first find the spring constant (k) using the given information. We know that the spring stretches by 9.76811 cm when a load of 17.9936 N is suspended from it.
Rearranging Hooke's Law, we have:
k = F / x
Substituting the values, we get:
k = 17.9936 N / 9.76811 cm
Now, we can use this spring constant to calculate the amount of stretch when a load of 65.8458 N is suspended from the spring after it is cut in half.
Again, using Hooke's Law:
F = k * x
Rearranging the equation, we can solve for x:
x = F / k
Substituting the values, we get:
x = 65.8458 N / k
Finally, substituting the calculated value of k, we can find the value of x:
x = 65.8458 N / (17.9936 N / 9.76811 cm)
Simplifying the expression, we find:
x ≈ 33.8 cm
Therefore, the spring will stretch by approximately 33.8 cm when a load of 65.8458 N is suspended from it after it is cut in half.