A spiral spring has a lenght of 14cm when a load of 4N is hung on it.A force of 6N extends the spring by 4cm.calculate the unstretched lenght of the spring.
xi is initial length
x is total length with stretch
x-xi is stretch
F = k(x-xi)
4 = k (14 -xi)
6 = k(4)
k = 6/4 = 3/2
4 = (3/2)(14-xi)
8 = 42 -3xi
3 xi = 34
xi = 11 1/3
A spiral spring extends by5 cm under a load of 60N when the load is replaced by a still block then new extension is 7cm . Caculate the weight of the still block
To calculate the unstretched length of the spring, we can use Hooke's law, which states that the force applied to a spring is proportional to the extension of the spring.
Hooke's Law:
F = -kx
Where:
F = Force applied to the spring
k = Spring constant
x = Extension of the spring
From the given information, we can set up two equations using Hooke's law:
Equation 1: 4N = -k(4cm)
Equation 2: 6N = -k(4cm + x)
From Equation 1, we can solve for the spring constant (k):
-4k = 4N
k = -1N/cm
Now, we can substitute this value of k into Equation 2 and solve for x:
6N = -(-1N/cm)(4cm + x)
6N = 4cm + x
x = 6N - 4cm
x = 2cm
Since the unstretched length of the spring is the sum of the extension (4cm) and the extension caused by the load (2cm), we can calculate the unstretched length:
Unstretched length = 4cm + 2cm
Unstretched length = 6cm
Therefore, the unstretched length of the spring is 6cm.
To calculate the unstretched length of the spring, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the extension of the spring.
Hooke's Law can be expressed as:
F = k * x
Where:
F = Force applied to the spring
k = Spring constant (a measure of the stiffness of the spring)
x = Extension of the spring
In this case, we have two sets of values:
Case 1:
F1 = 4N (load)
x1 = 4cm (extension)
Case 2:
F2 = 6N (force)
x2 = 4cm (extension)
From the given information, we can set up two equations:
For case 1:
4N = k * 4cm
For case 2:
6N = k * 4cm
We can solve these two equations to find the value of k (the spring constant).
Divide the second equation by the first equation:
6N / 4N = k * 4cm / k * 4cm
1.5 = 1
Since both sides of the equation are equal, we can conclude that the spring constant (k) is the same in both cases.
Now, we can substitute the value of F1 and x1 into the first equation to find k.
4N = k * 4cm
Rearranging the equation gives us:
k = 4N / 4cm
k = 1 N/cm
Now that we know the spring constant (k), we can substitute it into either equation to find the unstretched length (x0) of the spring.
Using case 1:
4N = 1 N/cm * x0
x0 = 4N / 1 N/cm
x0 = 4 cm
Therefore, the unstretched length of the spring is 4 cm.