Two springs have force constant K1&K2 (K1>K2) .each spring is extended by same farce F. If their elastic potential energy are E1&E2then E1/E2)is?
To find the ratio of elastic potential energies (E1/E2), we need to consider the formulas for elastic potential energy in springs.
The elastic potential energy (E) stored in a spring can be calculated using the formula:
E = (1/2) * k * x^2
where E is the elastic potential energy, k is the force constant of the spring, and x is the displacement or extension of the spring.
Given that two springs have force constants K1 and K2 (K1 > K2) and are extended by the same force F, we need to find the ratio E1/E2.
Let's calculate the elastic potential energy for the first spring (E1) using the formula above:
E1 = (1/2) * K1 * x^2 ------- (equation 1)
Now, let's calculate the elastic potential energy for the second spring (E2) using the same formula:
E2 = (1/2) * K2 * x^2 ------- (equation 2)
Since both springs are extended by the same force F, the extensions x1 and x2 for each spring will be the same. Hence, we can remove x from the equations and focus on the force constants:
E1 = (1/2) * K1 * x^2
and
E2 = (1/2) * K2 * x^2
Now, let's calculate the ratio E1/E2 by dividing equation 1 by equation 2:
(E1/E2) = [(1/2) * K1 * x^2] / [(1/2) * K2 * x^2]
The (1/2) term cancels out, as well as the x^2 term:
(E1/E2) = (K1/K2)
Therefore, the ratio of the elastic potential energies (E1/E2) is equal to the ratio of their force constants (K1/K2).
Answer: E1/E2 = K1/K2