An 8N force stretches a spring to the 20cm Mark on the meter rule. If the extension on the spring is 4cm, calculate original length of the spring and extension produced by a 10N force
To solve this problem, we can use Hooke's Law, which states that the force applied to a spring is directly proportional to the extension produced. Mathematically, this 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 extension produced.
In this case, we know that the force applied to stretch the spring to the 20 cm mark on the meter rule is 8N, and it produces an extension of 4 cm. So we can write:
8N = k * 4cm
Now we can solve for the spring constant k. Dividing both sides of the equation by 4cm gives:
k = 8N / 4cm
k = 2 N/cm
Now that we know the spring constant, we can use it to find the original length of the spring and the extension produced by a 10N force.
Let's assume the original length of the spring is L cm. The extension produced by a 10N force can be calculated using the formula:
10N = k * x
Substituting the known values:
10N = 2 N/cm * x
Simplifying, we find:
x = 10N / 2 N/cm
x = 5 cm
Therefore, the original length of the spring is L cm, and the extension produced by a 10N force is 5 cm.