Free Fall Methods Investigation
I am going to use three different methods in which I will find the value of gravity (g). Then I am going to compare all three methods to see which is the best. The three experiments will be
Is motion with no acceleration other than that provided by gravity, and no deceleration other than that caused by the aerodynamic drag of the object (hence the term also applies for moving up). In skydiving, the term is also applied to the period of the jump before the parachute is opened, and in colloquial usage, falling through an atmosphere is normally considered to be free fall.
Example of free fall:-
An object dropped in a vacuum tube
Things that are not at fee fall:-
Jumping from an airplane: there is a resistance force provided by the atmosphere.
Oscillations are plentiful in our natural world - we see them everywhere
When you throw a stone into a puddle ripples to spread out to the edges. When you pluck a guitar string, the string vibrates back and forth. When you touch a tree branch it oscillates.
When you rock a small boat, it wobbles to and fro in the water before coming to rest again. When you stretch out a spring and release it, the spring goes back and forth between being compressed and being stretched out.
Oscillation is the natural world’s way of returning a system to its equilibrium position - the stable position of the system where the net force acting on it is zero. If you throw a system off-balance, it doesn’t simply return to the way it was; it oscillates back and forth about the equilibrium position. The system oscillates as a way of giving off energy. A system that is oscillating has been given extra energy by some outside force - it has more energy than a system in its equilibrium position.
The movement of an oscillating body is called 'harmonic motion'. SHM and Circular motion
The motion is uniform circular motion, meaning that the angular velocity is constant, and the angular displacement is related to the angular velocity by the equation:
Plugging this in to the x and y positions makes it clear that these are the equations giving the coordinates of the object at any point in time, assuming the object was at the position x = r on the x-axis at time = 0:
An object experiencing simple harmonic motion is traveling in one dimension, and its one-dimensional motion is given by an equation of the form
The amplitude is simply the maximum displacement of the object from the equilibrium position. So, in other words, the same equation applies to the position of an object experiencing simple harmonic motion and one dimension of the position of an object experiencing uniform circular motion. Note that the in the SHM displacement equation is known as the angular frequency. It is related to the frequency (f) of the motion, and inversely related to the period (T):
The simple pendulum
A simple pendulum is a pendulum with all the mass the same distance from the support point, like a ball on the end of a string. Gravity provides the restoring force (a component of the weight of the pendulum).
Summing torques, the restoring torque being the only one, gives:
For small angular displacements :
So, the torque equation becomes:
Whenever the acceleration is proportional to, and in the opposite direction as, the displacement, the motion is simple harmonic. For a simple pendulum, with all the mass the same distance from the suspension point, the moment of inertia is:
The equation relating the angular acceleration to the angular displacement for a simple pendulum thus becomes:
This gives the angular frequency of the simple harmonic motion of the simple pendulum, because:
Hooke’s law states that the extension of a spring (e) is proportional to the tension (T) which produced it.
T = K x e
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