Solution to "Injection-Molding Process Control"

Task a)

There are many different variants which can be imagined. 

Using a linear encoder with two LEDs under pretension by a spring, pressing the block in a defined position:

Advantage: Simple setup, very much comparable ot a standard length-measurement

Disadvantage: Friction may block the measurement if not designed well

Using a capacitive sensor with the brick between two plates, being in contact with both of them.

Advantage: Very simple setup, distance measurement should be possible

Disadvantage: e_r changes with the density of the brick

Doing a light-distance measurement based on a laser-diode reflecting at the surface of the brick. Light then detected with a light-detection array or a light-sensing resistor.

Advantage: Contact-free measurement

Disadvantage: May be challenging when brick color or surface quality changes

Task b)

The point of 70% is on the logarithmic scale somewhere in the range of 130 line/pairs per mm. This is a resolution of 7.7 µm.

Task c)

The nominal length is 20 mm. Consequently the nominal weight should be 10.5 gramms. The measurement uncertainty is +/- 0.1 grams. 

Task d) 

The weight measurement of +/- 0.1 grams equals a length change which could be +0.2 mm (e.g. a weight of 10.6 grams could also occur at 20.2 mm). This is inacceptable considering the requirement of 10 µm for measurement.