A block on a spring oscillates with a period of 1.5 seconds. If the mass of the block is halved, what will be the new period?
Practice Questions
1 question
Q1
A block on a spring oscillates with a period of 1.5 seconds. If the mass of the block is halved, what will be the new period?
1.5 s
1.22 s
1.73 s
1.0 s
The period of a mass-spring system is T = 2π√(m/k). Halving the mass does not change the period since it is independent of mass in this case.
Questions & Step-by-step Solutions
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Q
Q: A block on a spring oscillates with a period of 1.5 seconds. If the mass of the block is halved, what will be the new period?
Solution: The period of a mass-spring system is T = 2π√(m/k). Halving the mass does not change the period since it is independent of mass in this case.
Steps: 7
Step 1: Understand that the period of a mass-spring system is given by the formula T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant.
Step 2: Note that the original period is 1.5 seconds with a certain mass (let's call it m) and spring constant (k).
Step 3: If the mass is halved, the new mass becomes m/2.
Step 4: Substitute the new mass into the formula: T_new = 2π√((m/2)/k).
Step 5: Simplify the equation: T_new = 2π√(m/(2k)).
Step 6: Notice that the new period T_new is still dependent on the spring constant k, but the factor of 1/√2 comes from halving the mass.
Step 7: Realize that the period does change because it is now multiplied by 1/√2, which means the new period is shorter than the original period.
