Two springs A and B having constants 100 N/m and 600 N/m respectively arestretched by applying a force of equal magnitude. If the energy stored in spring A is216 J, estimate the energy stored in spring B.
Question
Two springs A and B having constants 100 N/m and 600 N/m respectively arestretched by applying a force of equal magnitude. If the energy stored in spring A is216 J, estimate the energy stored in spring B.
Solution
The energy stored in a spring is given by the formula:
E = 1/2 * k * x^2
where E is the energy, k is the spring constant, and x is the displacement or stretch of the spring.
Given that the energy stored in spring A (kA = 100 N/m) is 216 J, we can solve for x:
216 J = 1/2 * 100 N/m * x^2 x^2 = 216 J / (1/2 * 100 N/m) x^2 = 4.32 m^2 x = sqrt(4.32 m^2) x = 2.08 m
Now, we know that the same force is applied to spring B (kB = 600 N/m), so the displacement x will be the same. We can now calculate the energy stored in spring B:
EB = 1/2 * 600 N/m * (2.08 m)^2 EB = 1/2 * 600 N/m * 4.3264 m^2 EB = 1297.92 J
So, the energy stored in spring B is approximately 1298 J.
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