(c) The period of vibration for an object suspended from a spring is T = 2𝜋m/k where k is the force constant of the spring and m is the mass of the object. Therefore, to have a period T = 1.9 s when suspended from a spring with a force constant k = 10 N/m, the required mass ism = kT24𝜋2 = N/m2 s 2 4𝜋2 = kg.(d) We are given the spring constant k, which is the same on Earth and on Mars. We can see from the equation above that the mass depends only on the spring constant, the given period, and the constant 4𝜋2. Consequently, whether on Earth or on Mars, the same mass is needed for a period of T = 1.9 s.mEarth = mMars = kg.
Question
(c) The period of vibration for an object suspended from a spring is T = 2𝜋m/k where k is the force constant of the spring and m is the mass of the object. Therefore, to have a period T = 1.9 s when suspended from a spring with a force constant k = 10 N/m, the required mass ism = kT24𝜋2 = N/m2 s 2 4𝜋2 = kg.(d) We are given the spring constant k, which is the same on Earth and on Mars. We can see from the equation above that the mass depends only on the spring constant, the given period, and the constant 4𝜋2. Consequently, whether on Earth or on Mars, the same mass is needed for a period of T = 1.9 s.mEarth = mMars = kg.
Solution
The question is asking for the mass of the object that would result in a period of 1.9 seconds when suspended from a spring with a force constant of 10 N/m.
The formula given is T = 2𝜋√(m/k). We can rearrange this formula to solve for m, the mass of the object.
m = (T^2 * k) / (4𝜋^2)
Substituting the given values into the formula:
m = (1.9^2 * 10) / (4𝜋^2)
Calculate the above expression to find the mass.
For part (d), the question states that the spring constant is the same on Earth and Mars. Therefore, the mass required to achieve a period of 1.9 seconds would be the same on both planets. This is because the formula for the period of a spring does not depend on gravity, so the location (Earth or Mars) does not affect the mass required.
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