A spiral spring has a length of 14cm when a load of 4N is hung on it.A force of 6N extends the spring by 4cm.calculate,the length of the spring.if a force of 3N is hung on it;assuming hooke's law is obeyed
F = k (L - Li)
6 = k (4)
k = 6/4 = 3/2 Newtons/ cm extension
4 = (3/2) ( 14 - Li)
4 = 21 - 1.5 Li
1.5 Li = 117
Li = 11.33 cm initial length of spring with no force
so
3 = 1.5( L - 11.33)
3 = 1.5 L - 17
1.5 L = 20
L = 13 1/3 cm
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 or compression of the spring.
Given information:
Load: 4N
Extension: 4cm
Length: 14cm
Using Hooke's Law, we can set up a proportion to find the spring constant:
Force / Extension = Spring Constant
4N / 4cm = Spring Constant
Spring Constant = 1 N/cm
To find the length of the spring when a force of 3N is applied, we can set up another proportion:
Force / Extension = Spring Constant
3N / x = 1 N/cm
Cross multiplying, we get:
3N * 1 N/cm = x
x = 3 cm
Therefore, the length of the spring when a force of 3N is applied is 3cm.
To solve this problem, we can use Hooke's law, which states that the force exerted by a spring is directly proportional to its extension.
Hooke's law can be represented as:
F = kx
Where:
F = force exerted on the spring (N)
k = spring constant (N/m)
x = extension of the spring (m)
First, we need to find the spring constant (k) using the information given:
A spiral spring has a length of 14 cm when a load of 4 N is hung on it.
We can assume that when there is no force applied (x = 0), the spring is in its natural/original length. So we have:
14 cm = 0 m (Since x = 0)
Next, a force of 6 N extends the spring by 4 cm:
4 cm = 0.04 m (Since 1 cm = 0.01 m)
Now we can use Hooke's law to find the spring constant (k):
6 N = k * 0.04 m
Divide both sides by 0.04 m:
k = 6 N / 0.04 m
k = 150 N/m
Now, let's find the length of the spring when a force of 3 N is hung on it:
We need to find the extension (x) of the spring. Rearranging Hooke's law, we get:
x = F / k
Substituting the given values:
x = 3 N / 150 N/m
x = 0.02 m
Finally, we can find the total length of the spring by adding the extension (x) to the natural length:
Total length = Natural length + Extension
Total length = 14 cm + 0.02 m
Total length = 14.02 cm
Therefore, the length of the spring, when a force of 3 N is hung on it, is 14.02 cm.