A spiral spring extends from length 10.01m to 10.00cm when a force of 20N is applied on it. Calculate the constant force
k = 20N/(10.01-0.10) = 2.02 N/m = Force constant or spring constant.
Original Length,L_1= 10.00cm=0.1m
After extension, L_2=10.01cm=0.1001m
Force applied,F= 20N
e=L_2 - L_1
E= 0.1001 -0.1
E= 0.0001m
F=Ke
K=F/e
K=20/0.0001
K=200,000
K=2×10^5 Nm^-1
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A spiral spring extend from a length of 100cm to 10.01cm when a Force of 20Nus applied on it calculate the Force constant of the spring
The first step is to find the extension of the spring, which is the difference between the final length and initial length:
Extension = Final length - Initial length
Extension = 10.01 cm - 100 cm
Extension = -89.99 cm (Note that the extension is negative, indicating that the spring is compressed rather than stretched)
The next step is to use Hooke's Law, which states that the force exerted by a spring is proportional to its extension:
F = kx
where F is the force, k is the spring constant, and x is the extension. We can use this formula to solve for the spring constant:
k = F/x
k = 20 N / (-89.99 cm)
k = -0.222 N/cm (The negative sign indicates that the force and the extension are in opposite directions)
Alternatively, we can convert both the force and the extension to SI units:
Extension = -89.99 cm = -0.8999 m
k = 20 N / (-0.8999 m)
k = -22.22 N/m (The negative sign still indicates that the force and the extension are in opposite directions)
Therefore, the force constant of the spring is either -0.222 N/cm or -22.22 N/m, depending on the choice of units.
The total length of a spring when a mass of 20g is hung from its end is 14cm, while it's total length is 16cm when a mass of 30g is hung from the end calculate the unstreched length of the living assuming hooke's law obeyed
Let's first find the extension of the spring for each mass:
For a mass of 20g:
Total length = 14cm
Unstretched length = let's call this L
Extension = Total length - Unstretched length = 14 - L
For a mass of 30g:
Total length = 16cm
Unstretched length = L
Extension = Total length - Unstretched length - Extension for 20g mass = 16 - L - (14 - L) = 2cm
Now, we can use Hooke's Law, which states that the extension of a spring is directly proportional to the applied force (mass, in this case):
F = kx
where F is the force, k is the spring constant, and x is the extension. We can use the two sets of data to form two equations:
20g = 0.02 kg
30g = 0.03 kg
For the 20g mass:
0.02g * 9.81 m/s^2 = k * (14 - L) (converting to SI units)
For the 30g mass:
0.03g * 9.81 m/s^2 = k * 2
Simplifying, we get:
0.1962 - 0.01962L = 0.02k
0.2943 = 0.03k
Solving for k, we get:
k = 9.81 N/m
Now we can use either equation to solve for the unstretched length:
0.1962 - 0.01962L = 0.02 * 9.81
0.1962 - 0.1962L = 0.1962 - 3.924
L = 10cm
Therefore, the unstretched length of the spring is 10cm.
A Force of 15N stretch a spring to a total length of 30cm .an additional Force of 10N stretches the spring 5cm further find the natural length of the spring
Let's use Hooke's Law to find out the spring constant. Hooke's Law states that:
F = kx
where F is the force applied to the spring, k is the spring constant, and x is the extension of the spring.
For the first case, where a force of 15N stretches the spring to 30cm:
x = 30cm - L (L is the natural or unstretched length of the spring)
F = 15N
Using Hooke's Law, we get:
15N = k(30cm - L)
For the second case, where an additional force of 10N stretches the spring 5cm further:
x = 30cm + 5cm - L
F = 15N + 10N = 25N
Using Hooke's Law again, we get:
25N = k(30cm + 5cm - L)
Now we have two equations and two unknowns (k and L). We can solve for L by eliminating k. Rearrange the first equation to solve for k:
k = 15N / (30cm - L)
Substitute this expression for k into the second equation:
25N = (15N / (30cm - L))(30cm + 5cm - L)
Simplify and solve for L:
25N = (15N / (30cm - L))(35cm - L)
25N(30cm - L) = 15N(35cm - L)
750cmN - 25NL = 525cmN - 15NL
10NL = 225cmN
L = 22.5cm
Therefore, the natural length of the spring is 22.5cm.