hat is the period of a simple pendulum that is 1.13-m long in each situation? In an elevator accelerating at 2.41 m/s22.41 m/s2 upward
Question
What is the period of a simple pendulum that is 1.13-m long in each situation?
In an elevator accelerating at 2.41 m/s² upward
Solution
The period of a simple pendulum is given by the formula:
T = 2π √(L/g)
where: T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
However, in this case, the pendulum is in an elevator that is accelerating upward. This means that the effective acceleration due to gravity is the sum of the actual acceleration due to gravity and the acceleration of the elevator.
So, the effective g (g') is:
g' = g + a
where: g is the acceleration due to gravity (approximately 9.81 m/s²), and a is the acceleration of the elevator (2.41 m/s²).
So, g' = 9.81 m/s² + 2.41 m/s² = 12.22 m/s²
Now, we can substitute L = 1.13 m and g' = 12.22 m/s² into the formula for T to find the period of the pendulum:
T = 2π √(1.13 m / 12.22 m/s²)
This will give you the period of the pendulum in the accelerating elevator.
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