If a load of 100N is applied to a wire the extension is 1.2m calculate the energy stored in the wire
k = f / x = 100 N / 1.2 m
energy = 1/2 * k * x^2
To calculate the energy stored in the wire, we need to use the formula:
Energy = (1/2) × k × e²
Where:
- Energy represents the stored energy in the wire
- k represents the spring constant of the wire
- e represents the extension of the wire
In this case, we are given that the load applied to the wire is 100N and the extension is 1.2m. However, we still need to find the spring constant (k) of the wire.
To find the spring constant, we can use Hooke's Law:
F = k × e
Where:
- F represents the force applied to the wire
- e represents the extension of the wire
- k represents the spring constant of the wire
In this case, we know that the force applied to the wire is 100N and the extension is 1.2m. Thus, we can rearrange the equation to solve for k:
k = F / e = 100N / 1.2m = 83.33 N/m (rounded to two decimal places)
Now that we have the spring constant, we can substitute it into the energy formula along with the given extension:
Energy = (1/2) × k × e²
= (1/2) × 83.33 N/m × (1.2m)²
= 59.99 Joules (rounded to two decimal places)
Therefore, the energy stored in the wire is approximately 59.99 Joules.
To calculate the energy stored in the wire, you need to use Hooke's Law and the formula for elastic potential energy.
Hooke's Law states that the extension of a wire is directly proportional to the applied force. The equation is given by:
F = k * x
Where:
F is the applied force (in this case, 100N),
k is the spring constant (which is a property of the wire), and
x is the extension (in this case, 1.2m).
To find the spring constant, you need to rearrange the equation:
k = F / x
Now, substitute the given values into the equation:
k = 100N / 1.2m
Simplify:
k ≈ 83.33 N/m
Now, you can find the energy stored in the wire using the formula for elastic potential energy:
Elastic potential energy (U) = 0.5 * k * x^2
Substitute the values:
U = 0.5 * (83.33 N/m) * (1.2m)^2
Simplify:
U = 0.5 * 83.33 N/m * 1.44m^2
Calculate:
U ≈ 71.99 Joules
Therefore, the energy stored in the wire is approximately 72 Joules.