Young's Modulus of Wire with 0.94 kN Load

In summary, Young's Modulus is a measure of the stiffness of a material and is typically measured in units of pressure. It can be calculated by dividing the applied stress by the resulting strain and is affected by factors such as material type, wire thickness, and temperature. Young's Modulus is important in materials science because it helps us understand material behavior and determine their suitability for different applications.
  • #1
mikefitz
155
0
A wire of length 4.95 m with a cross-sectional area of 0.103 cm^2 stretches by 6.55 mm when a load of 0.94 kN is hung from it. What is the Young's modulus for this wire?

FA = Y (delta L/L)

0.103 (cm^2) = 1.03 × 10-5 m^2
6.55 millimeters = 0.00655 meters

= 9221.4 N x 1.03 × 10-5 m^2 = .09498

0.00655m / 4.95m = 0.00132323232
.09498 / 0.00132323232 = 71.7787788 Pa ?

what did i do wrong?
 
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  • #2
[tex]\Delta l = \frac{Fl}{YA} \Rightarrow Y = \frac{Fl}{\Delta l A}[/tex].
 
  • #3
Y = 940N * 4.95m
------------
.00655m * 1.03(10^-5)m^2

Y = 6.90356083 × 10^10

Does this seem correct? thanks for the help
 
  • #4
Yes, it seems correct.
 

What is Young's Modulus of a wire?

Young's Modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. It represents the amount of stress that a material can withstand before it starts to deform. It is typically measured in units of pressure, such as pascals (Pa) or newtons per square meter (N/m²).

How is Young's Modulus calculated?

You can calculate Young's Modulus by dividing the applied stress by the resulting strain. The stress is typically measured in units of force per unit area (such as N/m² or Pa), while the strain is a dimensionless quantity that represents the change in length or shape of the material under stress. The resulting value is the Young's Modulus in units of pressure.

What is the significance of a load of 0.94 kN in relation to Young's Modulus?

A load of 0.94 kN (kilonewtons) refers to the amount of force applied to the wire in the experiment. This load is used to measure the resulting strain in the wire, which can then be used to calculate the Young's Modulus. The specific load used in an experiment may vary depending on the material and thickness of the wire.

What factors affect the Young's Modulus of a wire?

The Young's Modulus of a wire can be affected by a number of factors, including the type of material, the thickness of the wire, and the temperature at which the experiment is conducted. Generally, materials with higher stiffness and lower ductility will have higher Young's Modulus values. Additionally, increasing the temperature can decrease the Young's Modulus of some materials.

Why is Young's Modulus important in materials science?

Young's Modulus is an important property in materials science because it helps us understand the behavior of materials under stress and determine their suitability for specific applications. It can also be used to compare the stiffness and strength of different materials, and to predict how they will deform under different conditions. This information is crucial for designing and engineering structures and products that can withstand varying levels of stress and strain.

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