A load of 54 N attached to a spring hanging vertically stretches the spring 4.9 cm. The spring is now placed horizontally on a table and stretched 14 cm.
What force is required to stretch it by this amount?
It can be calculated by proportions:
54/4.9cm = F / 14cm
Solve for F (in N).
To find the force required to stretch the spring by a certain amount, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement.
Hooke's Law can be written as: F = k * x
Where:
F is the force applied to the spring
k is the spring constant
x is the displacement of the spring
We are given that a load of 54 N stretches the spring vertically by 4.9 cm. So, F = 54 N and x = 4.9 cm.
First, let's convert the displacement to meters:
x = 4.9 cm = 4.9/100 = 0.049 m
Now, we can rearrange Hooke's Law to solve for the spring constant:
k = F / x
Substituting the given values, we have:
k = 54 N / 0.049 m
k ≈ 1102.04 N/m
Now, we can find the force required to stretch the spring by 14 cm:
x = 14 cm = 14/100 = 0.14 m
Using Hooke's Law, we can substitute the values of k and x:
F = k * x
F = 1102.04 N/m * 0.14 m
F ≈ 154.29 N
Therefore, approximately 154.29 N of force is required to stretch the spring by 14 cm when placed horizontally on a table.
To find the force required to stretch the spring by a specific amount, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement.
Hooke's Law can be expressed as:
F = k * x
Where:
F is the force applied to the spring,
k is the spring constant, and
x is the displacement or stretch/compression of the spring.
Given that the load of 54 N stretches the spring by 4.9 cm vertically, we can calculate the spring constant (k) by rearranging the equation:
k = F / x
k = 54 N / 0.049 m
k ≈ 1102 N/m
Now, we can use this spring constant to find the force required to stretch the spring horizontally by 14 cm.
F = k * x
F = 1102 N/m * 0.14 m
F ≈ 154 N
Therefore, the force required to stretch the spring by 14 cm horizontally is approximately 154 N.