A simple pendulum is 9.00 m long.
(a) What is the period of simple harmonic motion for this pendulum if it is hanging in an elevator accelerating upward at 2.00 m/s2?
I keep getting 6.7, but it's wrong
If it is accelerating upward at that rate, the effective value g is
g' = g + a = 11.8 m/s^2
instead of 9.8 m/s^2.
The period will be 2 pi sqrt(L/g')= 5.48 s
Apparently you used g' = g - a. That only applies if the elevator is accelerating downwards.
To determine the period of a simple harmonic motion for a pendulum, we can use 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.
In this case, the pendulum is hanging in an elevator accelerating upward at 2.00 m/s^2. So, the effective acceleration acting on the pendulum will be the sum of the acceleration due to gravity (9.8 m/s^2) and the acceleration of the elevator (2.00 m/s^2).
Effective acceleration (a) = g + acceleration of elevator = 9.8 + 2.00 = 11.8 m/s^2
Now, we can substitute the values into the formula to find the period:
T = 2π√(L/a) = 2π√(9.00/11.8) ≈ 6.74 s
The period of the simple harmonic motion for this pendulum, when hanging in an elevator accelerating upward at 2.00 m/s^2, is approximately 6.74 seconds.