Download Additional Math and Theory Topics for Physics 112 Exam Review

Additional Math and Theory Topics for Physics 112 Exam Review
Note: some of these ideas are in the larger review document and just being emphasized here but some are
additional topics.
Graphs
The obvious purpose of a graph is to show us something visually. A time-position graph tells us
where an object is at certain times. Just choose a time, go up to the plot line (the best-fit line) and then
look over to the position values to see where the object is. And, from our knowledge of slopes, the steeper
the line the faster the object is moving. The same idea for a time-velocity graph: choose a time, up to the
plot line, over to the velocity values and you there you have it – the object’s velocity at that particular
time.
Now, think about this: by doing a slope calculation with a t-p graph we can find out the velocity
of the object – we can “translate” the position information into velocity information! The slope value tells
us the velocity. Why? Because the fraction to find slope is “change in y / change in x” and when we look
at the unit of the answer, it is “distance/time”, like m/s. So, t-p graph —> slope —> velocity.
And, by finding the area under the plot of a t-v graph, we are actually finding out how far the
object has travelled. We can “translate” the velocity info into distance info. Why? Because the formula to
find the area under plot line is base x height. Since the base of a t-v graph is in seconds and the height is
in m/s, the unit of the answer is in meters – distance! (Recall: d = vt) So, t-v graph —> area —> distance.
An actual question to find the distance from a t-v graph will be like: “How far does the object
travel from 3 s to 10 s.” Go up to the plot line from the 3 s mark and up to the plot line from the 10 s
mark. Now, chunk up the new shape you have just made into some triangles and some rectangles. Find
the area of the triangles (A = b h/2) and the area of the rectangles (A = b h). Finally, get the total area and
you have found the distance travelled by the object in the specified time span.
Mechanical Advantage
Simple machines seem to make us stronger. It is easier to move a heavy sofa up a long, gently
sloping ramp than to try and lift it straight up. The same amount of work is done but it seems easier
because the work is “spread out” – the person exerts a smaller force but for a longer distance.
The Ideal Mechanical Advantage of a simple machine is based on design drawings – how far
should my end (de) of the simple machine move and how far should the resistance end (dr) move. The
Actual Mechanical Advantage is based on actual use – the forces involved. How much force do I exert
(Fe) against my end of the hammer, for example, and what force does the hammer claws exert (Fr) against
the nail I want to pull out of the board? But, what if the handle is made of plastic and it bends a bit? Then
I will have to exert extra, unexpected force to get the nail out. When I’m using a pulley, what if dust and
metal grit have clogged the pulley wheels and I need to pull with extra force to lift the crate? On a ramp,
what if the surface is covered with carpet to protect the furniture being moved? Again, I must exert more
force than expected. For reasons like these, the AMA value of a simple machine is often less than the
IMA.
Recall: AMA = Fr / Fe IMA = de / dr
Eff = AMA / IMA x 100%