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A spring of 30cm is stretched to 40cm by a load of 60N, calculate the energy stored in the spring​

User Lynchie
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1 Answer

6 votes

Answer:

The energy stored in the spring is 0.03 Joules.

Step-by-step explanation:

The energy stored in a spring can be calculated using Hooke's Law and the formula for potential energy stored in a spring:

Potential Energy = 0.5 * k * x^2

Where:

k is the spring constant (also known as the stiffness constant)

x is the displacement from the equilibrium position

First, let's calculate the spring constant (k) using the given information:

Initial length of the spring (unstretched) = 30 cm = 0.30 m

Final length of the spring (stretched) = 40 cm = 0.40 m

Displacement (x) = 0.40 m - 0.30 m = 0.10 m

Now, we can calculate the spring constant (k) using Hooke's Law:

F = -k * x

Where F is the force applied and x is the displacement. In this case, the force applied (load) is 60 N and the displacement is 0.10 m:

60 N = -k * 0.10 m

k = -60 N / 0.10 m

k = -600 N/m

[Note: The negative sign indicates that the force exerted by the spring is in the opposite direction to the displacement.]

Now that we have the spring constant, we can calculate the potential energy stored in the spring using the formula:

Potential Energy = 0.5 * k * x^2

Potential Energy = 0.5 * (-600 N/m) * (0.10 m)^2

Potential Energy = 0.5 * 600 N/m * 0.01 m

Potential Energy = 3 N * 0.01 m

Potential Energy = 0.03 Joules

So, the energy stored in the spring is 0.03 Joules.

User Joseph Fraley
by
7.5k points
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