CAPA #1 solutions.
Here, I will provide "generic" solution. Since the numbers and some details vary a little,
your problems may look a wee bit different, but this solution should tell you enough to solve
to your particular questions are available through CAPA (on the login page,
click on "view previous set". Just be sure to fill in the set number first, before clicking!
This week I will write out pretty detailed solutions. In the future I may get a little more
"efficient", but if you're struggling with a problem and find these solutions are inadequate, by all
means contact one of us (Steve Pollock or Murray Holland or your TA or an LA.
..) and talk
about it. You should feel like these *make sense* to you, don't let any confusion slip by now!
You should ALWAYS try to solve problems using symbols only, even
) on "number crunching " problems. There are lots of reasons - it's easier to check
your work, it's easier to see if the units are correct, it's easier for a TA to see if you've made a
mistake, it's easier to see if various limits make sense, it's easier to see the PHYSICS when you
have a formula instead of plugging numbers in right away. It's how any professional, in any field,
will solve real life problems, even numerical ones. Get in the habit of this! We will ask exam
questions where we won't give any numbers, you will have to work on a symbolic level.
1) Just helping you learn CAPA syntax. CAPA requires a space between the number and the
units, but NO space between the number and the "E".
So e.g. 3.56m/s is no good (no space
before the units), and 3.56 E2 cm/s is no good (the space before the E is bad!) but 3.56E2 cm/s is
fine, and 3.56E2 cm*s^-1 is also fine.
2) A little review of a Calc I skill. The integral of x^n is 1/(n+1) * x^(n+1).
So integrating x^2 gives you (1/3)x^3.
Integrating x gives you (1/2)x^2.
Any constants in front just stay there.
Since there are upper and lower limits, you must evaluate the answer at the upper limit and
subtract the lower.
If this is NOT review for you, perhaps you want to chat with an instructor to make sure you're
going to be in good "math shape" this term. We really won't be using a ton of Calculus, but I'd
say you need at least the ability to figure out an integral like this one every now and again.
(What's more important is that you understand what an integral MEANS!)
3) Area, A is given, and A= 4 Pi r^2.
Volume is (4/3) Pi r^3.
Use the first formula to solve for "r" = Sqrt[A/4 pi]. Then plug the r you just found back in:
V = (4/3) Pi r^3 = (4/3) Pi
Just plug the numbers in your calculator.
4) How do you proceed in a problem like this? First, look clearly at what's being asked for: the
speed at some given time. So this makes me think about *KINEMATICS*, the very first thing
we learned in Phys 1110. Kinematics relates position, velocity, acceleration, and time. Knowing
some of these generally tells you about the others!