Final answer:
To determine the amount that spring s1 is stretched (Δx1s) when the elastic potential energy of the two springs is the same, we can equate their elastic potential energy and solve for Δx1s. Plugging in the given values, we find that Δx1s is equal to 0.202 m.
Step-by-step explanation:
To determine the amount that spring s1 is stretched (Δx1s) when the elastic potential energy of the two springs is the same, we need to equate the elastic potential energy of spring s1 to the elastic potential energy of spring s2.
The elastic potential energy of a spring is given by the formula:
PE = 0.5 * k * x^2
where PE is the elastic potential energy, k is the spring constant, and x is the compression or stretch distance of the spring.
Since the elastic potential energy should be the same for both springs, we can set up the following equation:
0.5 * k1 * Δx1s^2 = 0.5 * k2 * Δx2^2
where Δx1s is the stretch distance of spring s1, k1 is the spring constant of spring s1, Δx2 is the compression distance of spring s2, and k2 is the spring constant of spring s2.
Plugging in the given values, we can solve for Δx1s:
0.5 * k1 * 0.066^2 = 0.5 * 90.0 * Δx2^2
0.5 * k1 * 0.004356 = 0.5 * 90.0 * Δx2^2
k1 * 0.004356 = 45.0 * Δx2^2
k1 = 45.0 * Δx2^2 / 0.004356
From the given information, we know that the mass of the object is 0.275 kg.
Using the formula for the spring constant:
k = m * g / x
where k is the spring constant, m is the mass, g is the acceleration due to gravity, and x is the stretch or compression distance of the spring.
For spring s1, we can set up the equation:
k1 = 0.275 * 9.80 / 0.066
Solving for k1:
k1 = 40.909 N/m
Now we can substitute this value of k1 in the equation we derived earlier:
40.909 * 0.004356 = 45.0 * Δx2^2
Δx2^2 = 0.040816
Δx2 = sqrt(0.040816)
Δx2 = 0.202 m
Therefore, spring s1 will be stretched by 0.202 m when the elastic potential energy of the two springs is the same.