Galilean Relativity

SpringPhysics

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?

kuruman

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?

SpringPhysics

Isn't it just 0.40 m?

kuruman

Yup.