A copper (Young's modulus 1.1 x 1011 N/m2) cylinder and a brass (Young's modulus 9.0 x 1010 N/m2) cylinder are stacked end to end, as in the drawing. Each cylinder has a radius of 0.38 cm. A compressive force of F = 6100 N is applied to the right end of the brass cylinder. Find the amount by which the length of the stack decreases.
couldn't solve this..
To solve this problem, we need to use Hooke's Law, which states that the strain in an object is directly proportional to the stress applied to it. In this case, the stress is the compressive force and the strain is the change in length.
First, let's find the change in length for each cylinder individually.
For the brass cylinder:
We can use Hooke's Law to find the change in length.
Stress = Force / Area
Area = π * r²
Strain = Stress / Young's modulus
Given:
Force = 6100 N
Radius = 0.38 cm = 0.0038 m
Young's modulus for brass = 9.0 x 10^10 N/m²
Area = π * (0.0038)^2 = 4.523893421 x 10^-5 m²
Stress = Force / Area = 6100 N / (4.523893421 x 10^-5 m²) = 1.349360229 x 10^11 N/m²
Strain = Stress / Young's modulus = (1.349360229 x 10^11 N/m²) / (9.0 x 10^10 N/m²) = 1.499289143
The change in length for the brass cylinder is given by:
Change in length for brass = Strain * Original length
For the copper cylinder:
Using the same approach, we can find the change in length.
Given:
Young's modulus for copper = 1.1 x 10^11 N/m²
Stress = Force / Area = 6100 N / (4.523893421 x 10^-5 m²) = 1.349360229 x 10^11 N/m²
Strain = Stress / Young's modulus = (1.349360229 x 10^11 N/m²) / (1.1 x 10^11 N/m²) = 1.22669117
Change in length for copper = Strain * Original length
Finally, to find the total change in length for the stacked cylinders, we can add the individual changes in length together.
Total change in length = Change in length for brass + Change in length for copper
Substituting the values found above, we can calculate the total change in length.