Using the slope of a graph to solve problems.
There are several quantities in mechanics which are the derivative of another quantity. Some are:
1) the net force on an object is the derivative of the momentum of that object with respect to (wrt) time,
2) the net force on an object is the derivative of that object's potential energy with respect to position.
3) velocity is the derivative of position wrt time
4) acceleration is the derivative of velocity wrt time
To see how to use this information, let's use #1 as an example. If you are shown a graph of momentum (y axis) v.s. time (x axis), then the force on that object is the slope of the line. For #2, it would be a graph of potential energy (y) v.s. position (x). An example of the latter is HRW problem #37 on page 192.
There are several quantities in mechanics which are the derivative of another quantity. Some are:
1) the net force on an object is the derivative of the momentum of that object with respect to (wrt) time,
2) the net force on an object is the derivative of that object's potential energy with respect to position.
3) velocity is the derivative of position wrt time
4) acceleration is the derivative of velocity wrt time
To see how to use this information, let's use #1 as an example. If you are shown a graph of momentum (y axis) v.s. time (x axis), then the force on that object is the slope of the line. For #2, it would be a graph of potential energy (y) v.s. position (x). An example of the latter is HRW problem #37 on page 192.
posted by Dr9pt8 at 1:52 PM
0 Comments:
Post a Comment
<< Home