One end of a spring is attached to a wall and Jamie pulls on the other end of the spring with a force of 100 N, stretching the spring by 19.5 cm. If Jason takes the end of the spring off of the wall and they both pull the spring with a force of 100 N, how far will the spring stretch?
To determine how far the spring will stretch when both Jamie and Jason pull on it, we need to understand Hooke's Law. Hooke's Law states that the force required to stretch or compress a spring is directly proportional to the displacement or change in length of the spring.
Let's first calculate the spring constant, k, using the given information. The spring constant represents the stiffness of the spring and is a measure of how much force is required to stretch or compress the spring by a certain amount.
We can use Hooke's Law formula to calculate the spring constant:
F = k * x
Where:
F is the force applied (100 N),
k is the spring constant, and
x is the displacement or change in length (19.5 cm = 0.195 m).
So, rearranging the formula to solve for k:
k = F / x
k = 100 N / 0.195 m
k ≈ 512.82 N/m (rounded to two decimal places)
Now that we have the spring constant, we can determine how far the spring will stretch when both Jamie and Jason pull on it with a force of 100 N.
Using Hooke's Law formula again:
F = k * x
Where:
F is the force applied (100 N),
k is the spring constant (512.82 N/m), and
x is the displacement or change in length we want to find.
Rearranging the formula to solve for x:
x = F / k
x = 100 N / 512.82 N/m
x ≈ 0.195 m (19.5 cm) (rounded to two decimal places)
Therefore, the spring will stretch by approximately 0.195 meters (or 19.5 cm) when both Jamie and Jason pull on it with a force of 100 N.