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# Inkjet Printer Power and Rating Problem

An A4 inkjet printer uses ink cartridges with a mass of 250g supported by a carrier having a mass of 150g. The printer head is moved across the page by a motor driving through a toothed belt. It makes a single traverse of the page in 1s, which includes acceleration and deceleration times. The acceleration and deceleration zones at each end of its travel are 1cm long and the carriage is stationary for 0.2s at each end to allow the paper to advance. Sliding friction between the guide rails and the carrier is equivalent to a steady retarding force of 3N.

a) Sketch a graph of power vs. time for the motor driving the print head?

b) What is the RMS rating of the motor?

c) If the efficiency of the motor and drive system is 80% and it is fed through a transistor regulator at 12V, what is the mean current through this regulator when the printer is working continuously?

#### Solution Preview

In accelerating (1) and decelerating part (3):
v = a*t
a = acceleration or deceleration
t = time
s = distance = (1/2)*a*t^2
s1 = s3 = 1 cm = 1*10^(-2) m
t1 = t3 = sqrt(2s1/a) = sqrt(2*1*10^(-2)/a)
v^2 = 2*a*s1 = 2*a*1*10^(-2)
=> v = sqrt(2*a*1*10^(-2))
s2 = constant speed zone = 23 -2 = 21 cm
t2 = s2/v = ...

#### Solution Summary

This solution contains the methodology required in order to answer all three parts of this question. A step-by-step guide of the equations needed to solve for certain values is included for all three parts as well. In addition,for part (a), a diagram has been included as part of the required answer. Note that to view the diagram an attachment picture file (jpg) needs to be opened.

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