15.3 Pendulums and SHM Flashcards
What must a pendulum be like for shm to be in effect?
Simple which means:
- the bob must be small and of high mass (dense)
- a light inextensible string must be used
What provides the restoring force?
The weight of the bob, mgsinΘ when modelled
What else must be met for shm to be in effect for a simple pendulum (hint angle)
The angle Θ must be small (less than 10 degrees) so that the force is proportional to displacement
If these are met what is the equation for period of a simple pendulum?
T = 2π(squre root) L / g
where l = length of string (distance from pivot of suspension to centre of of bob)
g = 9.81 Nkg
How can we use pendulums to estimate the value of g? what is the setup?
A pivot with a light inextensible string and a pendulum bob. This system must also have an angle sensor.
How would this practical work?
1) Attach pendulum to an angle sensor connected to a computer. Measure the length L.
2) Displace the pendulum from its rest position by a small angle. The pendulum will oscillate with shm.
3) The angle sensor measures the bobs displacement from rest with time. Read off T from the computer generated graph. (If the computer only measures displacement do number of oscillations over time measured by stopwatch)
4) Rearrange T = 2π(square root)l/g for g and substitute your values in
How does mass effect the period for a pendulum shm ?
It doesn’t as T doesn’t depend on mass
How does length effect the period for a pendulum shm?
T^2 is proportional to L hence it increases with it
How does amplitude effect the period for a pendulum shm?
It doesn’t , T is not dependant on A
If we model a pendulum system so that Tension can be worked out, what would it look like?
A triangle with L as adjacent and T as hypotenuse. At the end of hypotenuse there is a bob which has a triangle of its own of the same angle as triangle described above. The adjacent is the mass and hypotenuse mgcostheta and opposite(restoring force) mgsintheta
