A spiral spring is compressed by 0.04m.calculate the energy stored in the spring,if the force constant is 100Nm-1
Please help me to solve it
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stored energy = 1/2 k x^2 = 1/2 * 100 N/m * (0.04 m)^2 ... Nâ‹…m ... Joules
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Well, well, isn't it a springy question! Let's crunch some numbers and find out how much energy this spring is storing.
The formula to calculate the energy stored in a spring is:
E = 1/2 * k * x^2
where E is the energy stored, k is the force constant (also known as the spring constant), and x is the compression or extension of the spring.
In your case, the force constant (k) is 100 Nm-1 and the compression (x) is 0.04 m. Let's plug those values in:
E = 1/2 * 100 Nm-1 * (0.04 m)^2
Now let's do the math:
E = 1/2 * 100 Nm-1 * 0.0016 m^2
E = 0.08 Joules
Voila! The energy stored in that compressed spring is approximately 0.08 Joules. Hope that springs some happiness into your calculations!
To calculate the energy stored in a compressed spring, you need to use Hooke's Law, which relates the force applied to the spring to the displacement of the spring. Hooke's Law states that the force F applied to a spring is proportional to the amount it is stretched or compressed, given by the equation:
F = -kx
Where:
F is the force applied to the spring (in Newtons),
k is the force constant or spring constant (in N/m or Nm-1), and
x is the displacement of the spring (in meters). Note that the negative sign is included to indicate that the force acts in the opposite direction to the displacement.
In this case, you are given that the spring is compressed by 0.04m and the force constant is 100Nm-1. To calculate the energy stored in the spring, you need to find the amount of work done in compressing the spring, which is equal to the area under the force-displacement graph.
The work done can be calculated using the equation:
W = (1/2) k x^2
Where:
W is the work done (in Joules),
k is the force constant or spring constant (in N/m or Nm-1), and
x is the displacement of the spring (in meters).
Let's substitute the given values into the equation:
W = (1/2) * 100 * (0.04)^2
W = (1/2) * 100 * 0.0016
W = 0.08 Joules
Therefore, the energy stored in the spring when compressed by 0.04m with a force constant of 100Nm-1 is 0.08 Joules.