Help with Calculating Young's Modulus Using Data

[ayaanle]

can anyone help me with this question...i am stuck


data for steal wire 1.72 m long and 0.4 mm diameter

load 10 20 30 40 50 60
extension 0.7 1.5 2.1 2.9 3.6 4.3

find youngs modulus?


i have this formula E=F/A*L/AL but don't know how to use it...

 

[LowlyPion]

Welcome to PF.

It would help if you had the right equation:
http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html#c2

A is your area - they give you the diameter.

F is your load - they give you a bunch of loads.

L is your length - they give you the length

ΔL is the change in length - they give you Δ's for various loads.

 

[nlightner]

Hello,

Calculating Young's modulus can be a bit confusing, but I am happy to help you with this question. Young's modulus is a measure of the stiffness of a material and is defined as the ratio of stress to strain. In this case, we will be using the data for the steel wire to calculate its Young's modulus.

First, let's define some terms. Load refers to the amount of force applied to the wire, which is measured in Newtons (N). Extension refers to the change in length of the wire, which is measured in meters (m). The diameter of the wire is also given, which we will need to calculate the cross-sectional area (A) of the wire.

To calculate the cross-sectional area, we will use the formula A = πr^2, where r is the radius of the wire. Since the diameter is given, we need to divide it by 2 to get the radius. In this case, the radius is 0.4 mm/2 = 0.2 mm = 0.0002 m. Substituting this value into the formula, we get A = 3.14*(0.0002)^2 = 0.000000125 m^2.

Now, we can use the formula for Young's modulus, E = (F/A)*(L/L0), where F is the load, A is the cross-sectional area, L is the length of the wire, and L0 is the original length of the wire (1.72 m in this case). We will use the data given for load and extension to calculate the stress (F/A) and strain (L/L0) values for each data point.

For the first data point (10 N, 0.7 m), stress = 10 N/0.000000125 m^2 = 80,000,000 N/m^2 and strain = 0.7 m/1.72 m = 0.407. Plugging these values into the formula, we get E = (80,000,000 N/m^2)*(0.407) = 32,560,000 N/m^2. Repeat this process for all data points and then take the average of all the calculated values to get the Young's modulus for the steel wire.

I hope this explanation helps you understand how to calculate Young's modulus using the given data. Let me know if you have any further questions