a force of 3.5 N is applied to a spring which obeys Hooke's law and produces and extension of 0.07m.
calculate the spring constant
what is the size of the force that will produce and extension of 4.0 cm
caluclate the unstretched length of the spring if its total length is 17.5 cm when applied force is 5 N.
The spring constant k = Force/extension.
In your case, k = 3.5/0.07 = 50 N/m
Use that k to calculate the force when the extension = 0.04 m. It should be (4/7) times 3.5 = ___ Newtons.
For the final question, calculate the extension when F = 5N,
extension = F/k = 0.1 m = 10 cm
and subtract that from 0.175 m to get the unstretched length.
To calculate the spring constant, we can use Hooke's law, which states that the force applied to a spring is directly proportional to the extension produced. The formula for Hooke's law is:
F = k * x
Where F is the applied force, k is the spring constant, and x is the extension produced.
1. To calculate the spring constant (k), we can rearrange the formula as:
k = F / x
Substituting the given values, we have:
k = 3.5 N / 0.07 m
k = 50 N/m
So, the spring constant is 50 N/m.
2. To calculate the force that will produce an extension of 4.0 cm, we can use the same formula:
F = k * x
Substituting the given values, we have:
F = 50 N/m * 0.04 m
F = 2 N
So, the force required to produce an extension of 4.0 cm is 2 N.
3. To calculate the unstretched length of the spring, we need to use the original formula and rearrange it to solve for x:
F = k * x
Substituting the given values (F = 5 N and total length = 17.5 cm = 0.175 m), we have:
5 N = k * x
To find x, we need to convert the total length of the spring to the stretched length by subtracting the extension produced:
Stretched length = Total length - Extension = 0.175 m - 0.07 m = 0.105 m
Now we can find x:
5 N = 50 N/m * x
x = 5 N / 50 N/m
x = 0.1 m
Since we already found the stretched length to be 0.105 m, we can find the unstretched length by subtracting the stretched length from the total length:
Unstretched length = Total length - Stretched length = 0.175 m - 0.105 m = 0.07 m
So, the unstretched length of the spring is 0.07 m.