Copper/Brass Cylinders: Compressive Force & Length Change

[benzimm86]

a copper cylinder(3 cm long) and a brass cylinder(5 cm long) are stacked end to end. each cylinder has a radius of .25 cm a compressive force of f=6500 N is applied to the right end of the brass where the other copper end is against a sollid object. find the amount by which the length of the stack decreases

 

[benzimm86]

my work

with brass being 9.0*10^10 and copper being 1.1*10^11 what i came up with was 5 cm (for the total length of the copper piece plus the brass piece) 3250 being half of the compression force and 9.9*10^21 for the brass and the copper

my equation is (5*3250)/(9.9*10^21)=1.6*10^-18

 

[wais]

The compressive force applied to the right end of the brass cylinder will cause it to deform and push against the copper cylinder. This will create a compressive force on the copper cylinder as well. Since the cylinders are stacked end to end, the compressive force will be distributed between the two cylinders.

To find the amount by which the length of the stack decreases, we can use the formula for strain, which is defined as the change in length divided by the original length. In this case, the original length of the stack is 8 cm (3 cm for the copper cylinder and 5 cm for the brass cylinder).

We can also use the formula for stress, which is defined as the force applied divided by the cross-sectional area of the material. The cross-sectional area of both cylinders can be calculated using the formula for the area of a circle (A=πr^2).

Using these formulas, we can set up the following equation:

Stress on brass = Stress on copper

(Force applied on brass)/(Area of brass) = (Force applied on copper)/(Area of copper)

(6500 N)/((π(0.25 cm)^2)) = (Force on copper)/((π(0.25 cm)^2))

Solving for the force on copper, we get:

Force on copper = (6500 N)(0.25 cm)^2/(0.25 cm)^2 = 6500 N

Since the force on the copper cylinder is the same as the force on the brass cylinder, the compressive force on the copper cylinder is also 6500 N.

Now, using the formula for strain, we can calculate the change in length of the stack:

Strain = (change in length)/(original length)

(Change in length)/(8 cm) = (6500 N)/(Young's modulus of copper)

Solving for the change in length, we get:

Change in length = (6500 N)(8 cm)/(Young's modulus of copper)

To find the Young's modulus of copper, we can use the fact that it is approximately 117 GPa (gigapascals).

Therefore, the change in length of the stack is approximately 44.4 micrometers (0.0444 mm).

In conclusion, the stack of copper and brass cylinders will decrease in length by approximately 44.4 micrometers when a compressive force of 6500 N is applied to the right end of the brass cylinder