A cable with a diameter of 6mm is used to lift crate. Calculate the mass of the crate required to create a stress of 350 MPa.
Let's begin with the definition of stress:
Stress = F/A
First, we need to recall that the force the weight of the crate will exert on the cable will be equal to:
F= m*g
We know the stress, g and A. Combining this we can write:
Stress = m*g/A
Rearrange for the mass:
A*Stress/g = m
We can calculate the cross-sectional area of the cable using the equation for the area of a circle:
Area = pi*r2
Remember to half the diameter and convert it into meters before calculating the area!
Area = pi*(0.006/2)2 = 2.827 * 10-5 m2
Now we sub everything in:
m = (2.827 * 10-5)(350106)/9.81
m = 1008.6kg
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