A spring is compressed a distance of 'x' stores 500J of energy. How much energy is stored in the spring if it is compressed a distance of 4x?
the energy is proportional to the SQUARE of the compression
4^2 = ?
To find the energy stored in the spring when it is compressed a distance of 4x, we can use the formula for potential energy stored in a spring, which is given by:
E = (1/2) * k * x^2
Where:
E is the energy stored in the spring,
k is the spring constant, and
x is the distance the spring is compressed.
We have been given that when the spring is compressed a distance of x, it stores 500J of energy.
Substituting the given values, we can write the equation as:
500 = (1/2) * k * x^2
To find the energy stored in the spring when it is compressed a distance of 4x, we need to substitute 4x for x in the equation.
Let's solve the equation to find the value of the spring constant, k.
To do this, divide both sides of the equation by (1/2) * x^2:
500 / [(1/2) * x^2] = k
Now, we can substitute 4x for x in the equation:
500 / [(1/2) * (4x)^2] = k
Simplify the equation:
500 / (1/2) * 16x^2 = k
500 / (8x^2) = k
To find the amount of energy stored in the spring when it is compressed a distance of 4x, substitute 4x for x in the equation for potential energy:
E = (1/2) * k * (4x)^2
Simplify the equation:
E = (1/2) * k * 16x^2
Now, substitute the value of k we found earlier:
E = (1/2) * (500 / (8x^2)) * 16x^2
Simplify the equation:
E = 500 * 2
E = 1000J
Therefore, when the spring is compressed a distance of 4x, it will store 1000J of energy.