An assembly line has a staple gun that rolls to the left at...

An assembly line has a staple gun that rolls to the left at $1.0 \mathrm{m} / \mathrm{s}$ while parts to be stapled roll past it to the right at $3.0 \mathrm{m} / \mathrm{s} .$ The staple gun fires 10 staples per second. How far apart are the staples in the finished part?

Key Concepts

Distance Calculation

The distance moved by an object over a given time period is found by multiplying its speed by the time elapsed. In this problem, once the effective relative speed is determined, multiplying it by the time interval between staples (derived from the firing rate) yields the spacing between the staples in the finished part.

Frequency and Time Interval

Frequency refers to how many events occur per second, while the time interval is the reciprocal of the frequency. Here, 10 staples per second means there is an interval of 0.1 seconds between each staple. This time interval is used to compute the distance between staples, as it determines the duration over which the part moves between successive staple firings.

Relative Velocity

Relative velocity is the measure of how fast one object is moving compared to another. In problems like this, where two objects move in opposite directions, understanding their relative velocity is essential to determine the effective speed at which one part of the system (such as a staple) is laid down relative to another moving component (the part being stapled).

Frames of Reference

Frames of reference are perspectives or coordinate systems used to measure and analyze motion. In this context, it is important to choose a frame (such as the moving part) to correctly account for the combined effects of the staple gun’s motion and the part’s motion when calculating the spacing of the staples.

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