P19093: Over-Bed Hospital Table
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# Feasibility Analysis

## Feasibility Analysis

What are the forces acting on the table?
Solution: Draw a free body diagram
Forces:
• Fa = Applied force
• Fg = Force of gravity
• Fn = Normal force
• Ff = Force of friction

Tabeletop Center of Gravity, Forces, and Moment Calculations

Using the defined engineering requirements, hand calculations were done to determine what weight the base, tabletop, and supporting rod need to be under different scenarios.

The overall dimensions, and Free-Body Diagram of external and internal forces on the table are shown.

There are 2 scenarios that need to be considered:

• Case 1: Table is fully expanded with distributed load
• Case 2: Table is in default position(half-moon shape) with load on one endpoint

Case 2 is the worst case scenario because the weight of the entire tabletop is located on one half of the entire bedside table.

Case 1 & 2 complete calculations for the moments, force, and total mass of the table:

The following shows what the mass of the base needs to be to support the mass of the tabletop. The mass of the base and tabletop is dependent of what the tabletop material is.

ABS Plastic (filled)

• Mass of table = 21.15 kg
• Moment at end of table = 156.84 Nm
• Mass of base = 30.27 kg

ABS Plastic (hollow)

• Mass of table = 21.09 kg

Calculations [here]

Poplar Wood (filled)

• Mass of table = 5.94 kg
• Moment at end of table = 96.004 Nm
• Mass of base = 15.01 kg

Density
We want to aim for a low density so we have a lightweight table.

• Poplar Wood = 300 kg/m^3
• Balsa Wood = 160 kg/m^3

Center of Gravity
Center of Gravity = (9.75 in, 20.19 in) Center of Mass = (7.377 in, 18.104 in)

## Supporting Rod Feasibility

What is the reactionary moment on the supporting rod?
Assumptions:

• Average laptop weight: 5 lbs (2.3 kg), we will use 3 kg weight
Equation: F = ma Supporting rod volume calculations [here]