|Oct2-09, 01:19 AM||#1|
1. The problem statement, all variables and given/known data
An assembly line has a staple gun that rolls to the left at 1.0 m/s while parts to be stapled roll past it to the right at 3.0 m/s. The staple gun fires 10 staples per second. How far apart are the staples in the finished part?
2. Relevant equations
r = r' + Vt
3. The attempt at a solution
I set the frames of reference to be the staple gun (S) and the part to be stapled (S'), assuming that their origins coincide at t = 0. The coordinate system will be right = positive. I think that the object is also the part to be stapled.
The velocity of the staple gun relative to the part will be -4.0m/s while the velocity of the part relative to the staple gun will be 4.0 m/s. (Do I need any formulas for that?)
The position of the part is then given by:
r = r' + Vt
Since I assumed that the origins coincided at t = 0, then position is:
r = Vt
So then substituting the velocity and assuming 1 sec has elapsed:
r = (4.0m/s)(1.0s)
r = 4.0 m
Since the staple gun fires 10 staples/sec, the distance between the staples should be 4.0 m/ 10 staples/sec, but that gives me 0.40 m*sec / staple.
Am I doing something wrong?
|Oct2-09, 05:11 PM||#2|
Look at it this way. Assume you are sitting on the staple gun. You look around and you see that there are parts moving past you at 4.0 m/s which means that for every second that goes by, 4 meters worth of parts move past you. You know that 10 staples are fired in that one second that goes by. Can you figure out the distance between staples now?
|Oct2-09, 05:19 PM||#3|
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