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

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

Step-by-step 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 =
`(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 =
`(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