Question

The tray dispenser in your cafeteria has broken and is not repairable. The custodian knows that you are good at design-ing things and asks you to help him build a new dispenser out of spare parts he has on his workbench. The tray dispenser supports a stack of trays on a shelf that is supported by four springs, one at each corner of the shelf. Each tray is rectangu-lar, with dimensions 45.3 cm by 35.6 cm. Each tray is 0.450 cm thick and has a mass of 580 g. The custodian asks you to design a new four-spring dispenser such that when a tray is removed, the dispenser pushes up the remaining stack so that the top tray is at the same position as the just-removed tray was. He has a wide variety of springs that he can use to build the dispenser. Which springs should he use

Answer 1

Answer:

 you have to find 4 spring with this elastic constant  k = 316 N / m

Explanation:

In this case for the design of the dispenser the four springs are placed in the four corner at the bottom, therefore we can use the translational equilibrium relationship

                    4 F_e -W = 0

               

where the elastic force is

                    F_e = k x

we substitute

                   4 kx = mg

                   k = $\frac{mg}{4x}$

Each tray has a thickness of x = 0.450 cm = 0.450 10⁻² m, this should be the elongation of the spring so that when the tray is in position it will remain fixed.

             

let's calculate

                  k = $\frac{0.580 \ 9.8}{4 \ 0.450 \ 10^{-2} }$

                  k = 3.1578 10² N / m

                  k = 316 N / m

therefore you have to find 4 spring with this elastic constant