A load of 59 N attached to a spring hanging vertically stretches the spring 5 cm. The spring is now placed horizontally on a table and stretched 14 cm. What force is required to stretch it by this amount?
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 expressed 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 from its equilibrium position
In this case, we are given two sets of information:
1. When a load of 59 N is attached to the spring and it hangs vertically, the spring stretches by 5 cm. This gives us one pair of values for force and displacement:
F1 = 59 N
x1 = 5 cm = 0.05 m
2. When the same spring is placed horizontally on the table, and it is stretched by 14 cm, we need to find the force required. Let's call this force F2 and the displacement x2:
x2 = 14 cm = 0.14 m
F2 = ?
We can use the given information to find the spring constant, k. Rearranging Hooke's Law equation, we get:
k = F / x
Using the first set of values, we can calculate k as:
k = F1 / x1
Substituting the values:
k = 59 N / 0.05 m = 1180 N/m
Now that we have the spring constant, we can use it to find the force, F2, required to stretch the spring by 0.14 m. Rearranging Hooke's Law equation, we have:
F2 = k * x2
Substituting the values:
F2 = 1180 N/m * 0.14 m = 164.8 N
Therefore, the force required to stretch the spring by 14 cm when placed horizontally on the table is approximately 164.8 N.