A block weighs 15 N and is suspended from a spring that is attached to the ceiling. The spring stretches by 0.075 m from its unstrained length. By how much does the spring stretch when a 24-N block is suspended from it?
To solve this problem, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position.
Hooke's Law equation:
F = k * x
Where:
F is the force applied to the spring,
k is the spring constant, and
x is the displacement from the equilibrium position.
In this case, we know that the spring stretches by 0.075 m when a 15-N block is attached to it. We need to find the displacement when a 24-N block is attached.
Using the equation above, we can set up a ratio to solve for the unknown displacement (let's call it x2):
15 N / 0.075 m = 24 N / x2
To solve for x2, we can cross-multiply and divide:
15 N * x2 = 0.075 m * 24 N
x2 = (0.075 m * 24 N) / 15 N
x2 = 0.12 m
Therefore, the spring stretches by 0.12 m when a 24-N block is suspended from it.
To determine the amount by which the spring will stretch when a 24-N block is suspended from it, we need to use Hooke's Law. Hooke's Law states that the force required to extend or compress a spring by a certain amount is directly proportional to that amount.
First, let's calculate the spring constant, k, of the spring. The spring constant represents the stiffness of the spring and is expressed in Newtons per meter (N/m).
We can use the formula:
k = F / x
where:
k = spring constant
F = force applied to the spring
x = displacement of the spring
Using the given information, we have:
F = 15 N (force applied)
x = 0.075 m (displacement)
Substituting these values into the formula, we find:
k = 15 N / 0.075 m
k = 200 N/m
Now that we have the spring constant, let's find out how much the spring will stretch when a 24-N block is suspended from it.
Again, we'll use Hooke's Law, but this time we'll rearrange the formula to solve for the displacement, x.
The formula becomes:
x = F / k
where:
x = displacement
F = force applied to the spring
k = spring constant
Using the given information, we have:
F = 24 N (force applied)
k = 200 N/m (spring constant)
Substituting these values into the formula, we find:
x = 24 N / 200 N/m
Performing the calculation gives us:
x = 0.12 m
Therefore, when a 24-N block is suspended from the spring, the spring will stretch by 0.12 meters.