A college dorm room measures 14 ft wide by 13 ft long by 6 ft high. What is the air in it under normal conditions?
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Answer:
Train accaleration = 0.70 m/s^2
Explanation:
We have a pendulum (presumably simple in nature) in an accelerating train. As the train accelerates, the pendulum is going move in the opposite direction due to inertia. The force which causes this movement has the same accaleration as that of the train. This is the basis for the problem.
Start by setting up a free body diagram of all the forces in play: The gravitational force on the pendulum (mg), the force caused by the pendulum's inertial resistance to the train(F_i), and the resulting force of tension caused by the other two forces (F_r).
Next, set up your sum of forces equations/relationships. Note that the sum of vertical forces (y-direction) balance out and equal 0. While the horizontal forces add up to the total mass of the pendulum times it's accaleration; which, again, equals the train's accaleration.
After doing this, I would isolate the resulting force in the sum of vertical forces, substitute it into the horizontal force equation, and solve for the acceleration. The problem should reduce to show that the acceleration is proportional to the gravity times the tangent of the angle it makes.
I've attached my work, comment with any questions.
Side note: If you take this end result and solve for the angle, you'll see that no matter how fast the train accelerates, the pendulum will never reach a full 90°!
If this case could ever happen, the speed would follow from this formula:
with f the frequency and lambda the wavelength. We are give a wavelength of 10m. The frequencies of the visible light can range between 400 to about 790 Terahertz, so let us pick a middle point of 600 THz ("green-ish") as a "representative."
The speed of such a wave would have to be 6e+15 m/s (which would be 7 orders of magnitude higher than the universal speed of light constant)