10.2.1 The Simple Pendulum Flashcards
The Simple Pendulum
- A simple pendulum is a point mass hung on an ideal string.
- The differential equation governing the motion of a simple pendulum is .
- Using the small-angle approximation, the differential equation describing a simple pendulum can be written in the same form as the differential equation describing simple harmonic motion. Thus, simple pendulums execute SHM, and all of our previous results on SHM apply.
A candelabra is hung from the end of a 10.0 m chain swinging with an initial amplitude of 0.10 rad and an initial velocity of 1 m / s. How high (maximum angle) will the candelabra swing?
theta = arccos( cos theta - v^2/2gl)
An inaccurate pendulum-driven grandfather clock shows two minutes and thirty seconds have elapsed when an accurate clock shows five minutes. Which of the following is the best way to make the grandfather clock accurate?
Increase the length by a factor of 4.
Which of the following pairs of equations applies to the forces involved in a simple pendulum?
T - mg(cos theta) =0
-g(sin theta) = a
An oddly paranoid man is locked in a room with only his clothes and a digital watch. Using his shoes, he constructs a simple pendulum 40.0 cm long with a mass of 1.00 kg. He hopes to determine whether he is on Earth or somewhere else. Which of the following is the most useful equation for measuring g under these circumstances?
g = l(2pi/T)^2
Consider the motion of a simple pendulum. Which of the following are the position(s) of all of the equilibrium points?
The upward and the downward vertical positions
An oddly paranoid man is locked in a room with only his clothes and a digital watch. Using his shoes, he constructs a simple pendulum 40.0 cm long with a mass of 1.00 kg. He hopes to determine whether he is on Earth or somewhere else. Which of the following is the equation for the angular velocity of this pendulum? Assume that the pendulum is simple and that A is the displacement from the vertical in meters.
w = -A0*sqrt(g/l)sin(sqrt(g/l))
A small tea bag is dunked in water and is now dangling at the end of its string. At what part of its trajectory is the kinetic energy a maximum?
At the bottom (the equilibrium point)
A man with a mass of 75.0 kg swings on the end of a 10.0 m rope and experiences SHM. Which of the following is affected by his mass?
total energy
In a physics lab, a student takes a 24.0 cm pendulum, ties a 500-g mass to it, displaces it pi/2 radians, and releases it. Which of the following best describes the resulting motion
This is not SHM.
