please show all work NEAT When working out these problems yo

please show all work (NEAT)

When working out these problems you must show all of your work. In general, for every formula you use, you should first show the formula, then show which numerical values you substitute into the formula, and where, and then the final numerical result. At least include the proper units in the end result of each numerical calculation. Finally, your work must be legible. The text should not be small and/or closely spaced. Problem 1) A square steel plate with the dimensions shown has a square hole and a round hole at the locations shown. The thickness of the plate (not shown) is 3.00 cm. We wish to find the Moment of Inertia of the square plate (with the holes) around an axis of rotation perpendicular to the page located at the center of the square hole. The volume mass density of steel is p 7850 kg/m (em) 3 Cm Ax of ion (AOR)-(perpendicular to the page)

Solution

1.

Using Pythagorus theorem, Edge length of the solid square plate a = sqrt (5² + 5²) = 7.071 cm²

Area of solid square plate A = a² = 7.071² = 50 cm²

Volume V = Area*thickness = 50*3 = 150 cm³ = 1.5*10^-4 m³

2)

Mass = Density*Volume

= 7850 * (1.5*10^-4)

= 1.1775 kg

3)

Moment of inertia of square lamina about its centre of mass I_cg = m*a² /6

Distance from centre of mass of solid plate to AOR = 5-3 = 2 cm

By parallel axis theorem, MOI of solid plate about AOR = m*a² /6 + m*2²

= 1.1775* 50 / 6 + 1.1775 * 4

= 14.5225 kg-cm² or 0.00145225 kg-m²

4)

Using Pythagorus theorem, Edge length of the solid square plate of the size of the square hole a = sqrt (1² + 1²) = 1.414 cm²

Area of small square hole A = a² = 1.414² = 2 cm²

Volume V = Area*thickness = 2*3 = 6 cm³ = 6*10^-6 m³