Tip:
Highlight text to annotate it
X
Welcome to lab 4. This time we are looking at using a new analysis on an old friend:
energy conservation on the Atwood machine.
Vectors are powerful, but they have a problem... You have to worry about directions! Even in
1D you have a negative sign! Wouldn't it be nice to work newtonian problems without the
vectors?
Let's introduce energy. It comes in two forms. This is potential energy. It is the stored
ability for something to do work. Being in a gravitational field gives us a potential
energy of the mass times the gravitational constant times the height. If we has a spring,
we would have a potential energy of 1/2 times the spring constant times the distance the
spring is displaced squared..
Kinetic energy is the energy of motion. It is the energy of moving objects. It is in
the following form: the kinetic energy is 1/2 times the mass times the velocity squared.
Notice the velocity is squared! As velocity increases, energy inceases faster and faster.
We also have other forms, such as rotational kinetic energy.
Energy is always conserved. It can change forms. If we can ignore things that take energy
out that are hard to account for, like heat energy from friction, then we can just use
the change in potential energy + kinetic energy change = 0, and then solve for v or whatever
we need to know. No vectors involved!
Let's start. Make sure you measure the height of the mass
at the start. Also measure the pulley height. You will also measure the mass of the string.
You'll need to have your scale well calibrated to measure such a small mass!
The position is now included on your graphs. You will need to click on each graph then
scale to fit to scale both correctly. Don't worry if a strange artifact appears on the
position graph.
You will measure ten points. You will get one time, one velocity, and one position from
each.
Do all 140 calculations in excel, so you only have to enter 7 calculations.
Put all three graphs, PE, KE, and E on one sheet. Linear fit the E graph, the other two
are poly order two.
You'll also try correcting for the string KE and the pulley KE and including that in
your Excel. You will not need to graph this. Does it make a difference to your result?
What about pulley and string PE?