An 8N force stretches a spring to the 20cm mark on a metre rule.if the extension on the spring is 4cm,calculate the original length of the spring?
To calculate the original length of the spring, we need to use Hooke's Law, which states that the force applied to a spring is directly proportional to the extension or compression of the spring.
Hooke's Law can be written as:
F = kx
where:
- F is the force applied to the spring,
- k is the spring constant (a measure of the stiffness of the spring), and
- x is the extension or compression of the spring.
In this case, the force applied to the spring is 8N, and the extension of the spring is 4cm (which is equivalent to 0.04m). We need to find the spring constant (k) in order to calculate the original length of the spring.
To find the spring constant, we can rearrange Hooke's Law and solve for k:
k = F / x
k = 8N / 0.04m
k = 200 N/m
Now that we have the spring constant, we can use it to find the original length of the spring. The formula to calculate the original length of the spring is:
x = (L - Lo)
where:
- x is the extension or compression of the spring,
- L is the final length of the spring (including the extension), and
- Lo is the original length of the spring.
In this case, the final length of the spring is 20cm (which is equivalent to 0.20m) and the extension is 4cm (which is equivalent to 0.04m).
Plugging the values into the formula, we get:
0.04m = (0.20m - Lo)
Rearranging the formula, we find:
Lo = 0.20m - 0.04m
Lo = 0.16m
Therefore, the original length of the spring is 0.16m.
I think the answer is 16cm but I don't know how
if the spring is extended 4 cm to the 20 cm mark
... it must have started at the 16 cm mark
an 8n force stretches a spring to the 20cm on a metre rule. if the extension on the spring is 4 cm, calculate the original length of the spring
Well, well, well, looks like our springy friend here is experiencing quite the stretch! Now, let's do some math magic to figure out its original length.
We know that the force applied is 8N and the extension on the spring is 4cm. To calculate the spring constant, we can use Hooke's Law: F = k * x, where F is the force, k is the spring constant, and x is the extension.
In this case, we have 8N = k * 0.04m (since 4cm is equal to 0.04m). Solving for k, we get k = 8N / 0.04m, which is equal to 200 N/m.
Now, to find the original length of the spring, we can use another equation: F = k * ΔL, where F is the force, k is the spring constant, and ΔL is the change in length.
In this case, we have 8N = 200 N/m * ΔL. Solving for ΔL, we find ΔL = 8N / 200 N/m = 0.04m.
Since the extended length is 0.04m and the original length is 0.20m, we can subtract the change in length from the extended length to find the original length of the spring.
Therefore, the original length of the spring is 0.20m - 0.04m = 0.16m. Voila!