How High Can a Tower of Sugar Cubes Be?

[pippintook]

Homework Statement

The Babblers have decided to build a tower that would reach the top of Rock Candy Mountain. For brick they used large sugar cubes ( = 1500 kg/m³). The compressive strength (stress) of sugar cubes is 6.0 MPa. How tall of a tower can the Babblers build?

Homework Equations

Stress = F/A = Y(ΔL/L₀)A

The Attempt at a Solution

I converted 6MPa to N/m² for 6,000,000 N/m², I just don't know how to find L. The A's cancel, leaving me with F = Y(ΔL/L₀), right? Is Y = 1500 kg/m^3?

 

[KLoux]

I'm not sure you're using the right equations... the stress relationship is OK (stress = F/A), but how is this related to the height? Show an equation that can relate the height of tower to some part of the stress equation.

-Kerry

 

[nlightner]

First, let's define some key terms. Stress is the force applied per unit area, and it is typically measured in units of N/m^2 or Pa (Pascals). In this case, the stress is the compressive force being applied to the sugar cubes per unit area.

Next, we need to understand the relationship between stress and height. As an object's height increases, the weight of the object (force) increases, and therefore the stress on the object increases as well. This is because the same amount of force is being applied to a smaller area as the object gets taller.

To calculate the maximum height of the tower, we need to use the equation for stress: Stress = F/A, where F is the force and A is the cross-sectional area of the sugar cubes. We know the stress (6 MPa) and the density of the sugar cubes (1500 kg/m^3), but we need to find the force (F) and the cross-sectional area (A).

To find the force, we can use the formula F = mg, where m is the mass of the sugar cube and g is the acceleration due to gravity (9.8 m/s^2). The mass of the sugar cube can be calculated by multiplying the density (1500 kg/m^3) by the volume of the cube, which can be found by using the formula V = l^3, where l is the length of one side of the cube.

Now, we can plug in our values to find the force:
F = (1500 kg/m^3)(l^3)(9.8 m/s^2)

To find the cross-sectional area, we can use the formula A = l^2, where l is the length of one side of the cube. We can also express this as A = (l/100)^2, where l is in centimeters. We need to convert the units from meters to centimeters in this case because the units for stress are typically in N/m^2.

Now, we can plug in our values to find the cross-sectional area:
A = (l/100)^2

Finally, we can substitute our values for force and cross-sectional area into the equation for stress and solve for the maximum height, l:
6,000,000 N/m^2 = (1500 kg/m^3)(l^3)(9.8 m/s^2)/[(l/100)^2]

S