A 200 MPa pressure is applied to a copper sphere with a radius of 2.0 cm. If the bulk modulus of copper is 130 GPa, calculate
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To calculate the change in volume of the copper sphere when a pressure is applied, we can use the formula:
ΔV = V * (ΔP / B)
Where:
ΔV = change in volume
V = initial volume
ΔP = change in pressure
B = bulk modulus
To find the initial volume of the sphere, we use the formula for the volume of a sphere:
V = (4/3) * π * r^3
Where:
V = initial volume
r = radius
Now let's calculate the initial volume of the copper sphere:
V = (4/3) * π * 2.0 cm^3
V = (4/3) * π * (2.0 cm)^3
V = (4/3) * 3.14 * 8 cm^3
V = 33.51 cm^3
Given:
Pressure, ΔP = 200 MPa
Bulk modulus, B = 130 GPa = 130,000 MPa
Now, let's calculate the change in volume:
ΔV = V * (ΔP / B)
ΔV = 33.51 cm^3 * (200 MPa / 130,000 MPa)
ΔV = 33.51 cm^3 * (0.00154)
ΔV = 0.0516 cm^3
Therefore, the change in volume of the copper sphere is 0.0516 cm^3.