A copper wire or length 2.0M, with cross-sectional area 7.1x10^-6 m^2 and youngs modulus of 11x10^10 N/m^2 has a 200 kg load hung on it. what is its increase in length?
F/A=Y* change in L/Length
= (200*9.8)/7.1x10^-6=11x10^10* delta L/2m? am i even setting this equation up right?
Yes, you are setting up the equation correctly using Hooke's Law. The formula is:
F/A = Y * (ΔL / L)
where F is the force applied (in this case, the weight of the load), A is the cross-sectional area of the wire, Y is the Young's modulus, ΔL is the change in length, and L is the original length of the wire.
Plugging in the given values:
F = 200 kg * 9.8 m/s^2 (gravitational acceleration) = 1960 N
A = 7.1 x 10^-6 m^2
Y = 11 x 10^10 N/m^2
L = 2.0 m
Now we can solve for ΔL:
(1960 N) / (7.1 x 10^-6 m^2) = (11 x 10^10 N/m^2) * (ΔL / 2.0 m)
ΔL = (1960 N) * (2.0 m) / (11 x 10^10 N/m^2 * 7.1 x 10^-6 m^2)
Calculating this expression will give you the increase in length of the copper wire.
Yes, you are setting up the equation correctly. You are using Hooke's Law, which states that the change in length of an object (delta L) is proportional to the applied force (F), the cross-sectional area of the object (A), and the Young's modulus (Y).
Let's solve for the change in length (delta L) in your equation:
First, calculate the force (F) acting on the wire:
F = mass x gravitational acceleration
F = 200 kg x 9.8 m/s^2
F = 1960 N
Next, substitute the values into the equation:
(1960 N) / (7.1x10^-6 m^2) = (11x10^10 N/m^2) x delta L / 2 m
Now isolate delta L:
delta L = [(1960 N) / (7.1x10^-6 m^2)] x [(2 m) / (11x10^10 N/m^2)]
Calculate the value:
delta L = 5.49295775x10^-5 m
Therefore, the increase in length of the copper wire is approximately 5.49295775x10^-5 meters.