A brass cube 6.0 cm on each side is placed in a pressure chamber and subjected to a pressure of 1.2×107 N/m2
on all of its surfaces. By how much will each side be compressed under this pressure?
2.9 * 10^ -6 m
To calculate the compression of each side of the brass cube under the given pressure, you need to use Hooke's Law and know the bulk modulus of brass.
Hooke's Law states that the compression or deformation of an object is directly proportional to the applied force. It can be expressed as:
ΔL = F / A * L
where ΔL is the change in length or compression, F is the force applied, A is the cross-sectional area, and L is the original length.
The bulk modulus (K) of a material measures its resistance to compression. The formula to calculate the compression is:
ΔL = -V * ΔP / K
where ΔL is the change in length, ΔP is the change in pressure, V is the volume, and K is the bulk modulus.
Here's how you can find the compression of each side of the brass cube:
1. Calculate the volume (V) of the cube:
V = (side length)^3 = (6.0 cm)^3 = 216 cm^3
2. Convert the pressure from pascals to newtons per square meter:
1.2 x 10^7 N/m^2 = 1.2 x 10^7 N/cm^2
3. Evaluate the bulk modulus (K) of brass. The bulk modulus for brass is roughly 9.8 x 10^10 N/m^2.
4. Calculate the change in length of each side using the formula:
ΔL = -V * ΔP / K
ΔL = -(216 cm^3) * (1.2 x 10^7 N/cm^2) / (9.8 x 10^10 N/m^2)
5. Convert the change in length to centimeters:
ΔL = -2.67 x 10^-4 cm
The negative sign indicates that the side of the cube is compressed. Therefore, each side of the brass cube will be compressed by approximately 2.67 x 10^-4 cm under the given pressure.