Question

Finding the radius based on height of my building and max angle of repose?

Height: 20 feet
Length: 200 feet
Width: 120 feet

Material:
Sand, Bank Damp ( angle of repose is 45 degrees)
Sand, Bank Dry ( angle of repose is 35 degrees)
Sand, core ( angle of repose 41 degrees)
Sand, foundry prepared ( 30 - 44 degrees)
Sand, Foundry shakeout (39 degrees)

Answer 1

To find the radius based on the height of the building and the maximum angle of repose, calculate the force of friction and use the moment of inertia equation for a solid cylinder.

Step-by-step explanation:

To find the radius based on the height of your building and the maximum angle of repose, you need to consider the equilibrium condition between the weight of the sand and the force of friction acting on it. The force of friction can be calculated by multiplying the weight of the sand by the coefficient of friction, which can be determined based on the angle of repose. The radius can then be found using the formula for the moment of inertia of a disk or a cylinder.

First, let's calculate the force of friction using the equation: force of friction = weight of sand * tan(angle of repose).

Next, determine the mass of the sand by dividing the weight by the acceleration due to gravity. Then, find the moment of inertia of a solid cylinder using the formula: moment of inertia = 0.5 * mass * radius^2.

Finally, rearrange the equation and solve for the radius to find the desired result.

Answer 2

The maximum angle of repose is the maximum angle at which a material can be piled without slumping. The material piled up will form a cone.

If we project the situation on a 2D plane, we get a triangle rectangle (see picture attached). We know one angle and the Opposite side (height) and we need to find the Adjacent side (radius).

Recalling trigonometry formulae:
tanα = O / A

Solving for A:
A = O / tanα

We can now substitute our data (O = 20):
1) Sand, Bank Damp
α = 45°
A = 20 / tan(45)
= 20
The radius is 20 feet.

2)Sand, Bank Dry
α = 35°
A = 20 / tan(35)
= 28.5629
The radius is 28.6 feet.

3) Sand, core
α = 41°
A = 20 / tan(41)
= 23.0074
The radius is 23 feet.

4) Sand, foundry prepared
α₁ = 30°
A₁ = 20 / tan(30)
= 34.6410

α₂ = 44°
A₂ = 20 / tan(44)
= 20.7106

The radius is between 20.7 and 34.6 feet.

5) Sand, Foundry shakeout
α = 39°
A = 20 / tan(39)
= 24.6979

The radius is 24.7 feet.