How Do You Solve a Dynamic Pulley System Problem?

[Roderic Day]

Homework Statement

http://img53.imageshack.us/img53/6141/41622697.png

Homework Equations

F = ma, all that basic stuff.

The Attempt at a Solution

Alright
g = 32.2
Ma = 150/g = 4.66lb
Mb = 75/g = 2.33lb

so Box A
__
|...}==== 2T
|__|

box B

3T
-----|...|______ 60lb
===={__|

Sum of Fx = ma

so for A
2T = 4.66aA
for B
60 - 3T = 2.33aB

then for the lengths of the wire I did
_________
O________
...n__O
|-sa-||sb|

so L = 2sa + 3sb
0 = 2aA + 3aB
but clearly aA and aB must have opposite signs so
2aA = 3aB

using simultaneous equations with the following you get
60 = 2.33aB +3T
0 = 4.66(3/2)aB - 2T
which makes aB = 7.22ft s-2 (ANS)
and T = 14.4 lb

then i figured there were two ways to go about work done

KEi(A+B) + Wd = KEf(A+B)
or Wd = 2T*sA + (60-3T)*sB

Which is great cause you get to doublecheck your result

the problem is that for method 1 I get 334.1J
and for method 2 I get 216.6J

So, yeah, any help is appreciated.

EDIT1: Formatting Errors
EDIT2: I found my mistake. My simultaneous eqs were wrong, it was 6.99, not 4.99.
Now the answers are aA = 7.02 ft s-2 and W = 140.4J
I'd still appreciate some double-checking on my method since I'm not really sure if I'm doing this right.

 

[anathema]

Hello there,

It looks like you have approached the problem correctly and have found your mistake in the simultaneous equations. Your revised answers for aA and W seem to be correct. In terms of double-checking your method, here are a few things to consider:

1. Make sure you are using the correct units throughout your calculations. I noticed a few inconsistencies in your units, so it's always good to double-check that they match up in each equation.

2. When using the equation KEi(A+B) + Wd = KEf(A+B), make sure you are using the correct values for KEi and KEf. In this case, KEi would be 0 since the boxes are initially at rest, and KEf would be the final kinetic energy of both boxes.

3. For the equation Wd = 2T*sA + (60-3T)*sB, make sure you are using the correct values for T, sA, and sB. It looks like you have used the correct values in your calculation, but just double-check to make sure.

Overall, it seems like you have a good understanding of the problem and have approached it correctly. Just be careful with your units and make sure you are using the correct values in each equation. Keep up the good work!

 

[tomcue]

I would like to commend you for your thorough approach to solving this problem. You have correctly identified the forces acting on the system and used Newton's second law to set up your equations. Your use of simultaneous equations is also a valid approach to solving the problem. Your mistake in the initial set up of the equations is a common one and it is great that you were able to identify and correct it.

In terms of your methods for calculating the work done, both approaches are valid and should give you the same answer. It is possible that there may be a small discrepancy due to rounding errors or slight variations in your calculations. I would suggest double-checking your calculations and using more precise values for your constants (such as using 9.8 m/s^2 for acceleration due to gravity instead of 9.81 m/s^2). Overall, your approach to solving this problem is sound and your final answer for the work done seems reasonable.