A structure known as a cantilever beam is clamped at one end but free at the other, analogous to a diving board that supports a swimmer standing on it (Figure P3.28). Using the following procedure, conduct an experiment to measure how the cantilever beam bends. In your answer, report only the significant digits that you know reliably.

(a) Make a small tabletop test stand to measure the deflection of a plastic drinking straw (your cantilever beam) that bends as a force F is applied to the free end. Push one end of the straw over the end of a pencil, and then clamp the pencil to a desk or table. You can also use a ruler, chopstick, or a similar component as the cantilever beam itself. Sketch and describe your apparatus, and measure the length L.

(b) Apply weights to the end of the cantilever beam, and measure the tip’s deflection Δy using a ruler. Repeat the measurement with at least a half dozen different weights to fully describe the beam’s force–deflection relationship. Penny coins can be used as weights; one penny weighs approximately 30 mN. Make a table to present your data.

(c) Next draw a graph of the data. Show tip deflection on the abscissa and weight on the ordinate, and be sure to label the axes with the units for those variables.

(d) Draw a best-fit line through the data points on your graph. In principle, the deflection of the tip should be proportional to the applied force. Do you find this to be the case? The slope of the line is called the stiffness. Express the stiffness of the cantilever beam either in the units lb/in. or N/m.

Figure P3.28

Transcribed Image Text:

F Ay L