Deflection and Modulus of Elasticity

In summary, the deflection at the end of the rod with dimensions 1m x 0.1m x 0.1m, when a load of 100N is applied and the modulus of elasticity is 1 x 1011 (N/m2), is 1 X 10-7 meters. This is calculated using the formula d = PL/AE, where d is the end deflection of the bar in meters, P is the applied load in Newtons, L is the length of the bar in meters, A is the cross sectional area of the bar in square meters, and E is the modulus of elasticity in N/m2.
  • #1
karmatic
18
0

Homework Statement


Calculate the deflection at the end of a rod whose dimensions are 1m x 0.1m x 0.1m, when a load of 100N is applied. The modulus of elasticity is given as 1 x 1011 (N/m2)


Homework Equations


d = PL/AE where

d = end deflection of bar in metres (in m)
P = the applied load in Newtons (N)
L = length of the bar (in m)
A = cross sectional area of bar (in m2)
E = modulus of elasticity (in N/m2)


The Attempt at a Solution



d = PL/AE
d = 100N x 1m/1-4(1 x 1011)
d = 100Nm/1-4 x 1 x 1-4 x 1011
d = 1-05

I'm not sure if I've calculated that in the right order, or if I have missed any steps. I'm a little bit lost on how to approach this problem!
 
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  • #2
Your approach is fine, but your maths is not so good. The Area of the rod is 1 X 10-2 m2 (that is, 0.01 m2). Please redo the maths and don't forget to note the units.
 
  • #3
Okay had another try at this one just now..

d=PL/AE
d=(1m*100N)/((1m*〖10〗^(-2))(1*〖10〗^11))
d=100Nm/((1m*1/100)(100000000000))
d=1/1000000
d=1^(-6)

I think that's the right answer, have I missed anything? The cross sectional area got me the first time round, pretty stupid mistake!

edit - I forgot the units for the final answer but I'm not sure what they should be, is it in metres?
 
  • #4
karmatic said:
Okay had another try at this one just now..

d=PL/AE
d=(1m*100N)/((1m*〖10〗^(-2))(1*〖10〗^11))
d=100Nm/((1m*1/100)(100000000000))
d=1/1000000
d=1^(-6)

I think that's the right answer, have I missed anything? The cross sectional area got me the first time round, pretty stupid mistake!

edit - I forgot the units for the final answer but I'm not sure what they should be, is it in metres?
If you stick with Newton and meter units, your result for the deflection should be in meters (PL/AE has units of N*m/((m^2)(N/m^2)) = N*m/N = m). You are off by a decimal point, the answer should be d = 1 X 10-7 m.. Watch your scientific notation, and keep track of the decimal point especially when using SI units of measure.
 
  • #5




Hello there! It looks like you have the right equation for calculating the deflection of a rod under a load. However, there are a few things to consider in order to correctly solve this problem.

First, it's important to note that the modulus of elasticity, E, is given in units of N/m2. This means that the units of the deflection, d, will also be in meters (m), not millimeters (mm) as in your attempted solution. So, your final answer should be 1.05 m, not 1.05 mm.

Second, the cross-sectional area of the rod, A, is given as 0.1m x 0.1m = 0.01m2, not 1m2. This is because the dimensions of the rod are given as 1m x 0.1m x 0.1m, not just 1m. So, your equation should be:

d = PL/AE
d = 100N x 1m/0.01m2 x 1 x 1011 N/m2
d = 1m/0.01-4 x 1011
d = 1.05 m

It's important to pay attention to units and make sure they are consistent throughout the calculation.

I hope this helps and good luck with your homework!
 

1. What is the definition of deflection?

Deflection refers to the displacement of a material or structure under applied load. It is a measure of how much the object bends or deforms under stress.

2. How is deflection related to modulus of elasticity?

Deflection is directly related to the modulus of elasticity, also known as Young's modulus. A higher modulus of elasticity means the material is stiffer and will experience less deflection under a given load.

3. Can deflection be calculated or predicted?

Yes, deflection can be calculated using equations and formulas based on known properties of the material and the applied load. However, the accuracy of these predictions may vary depending on the complexity of the structure and any unexpected factors that may affect the deflection.

4. What factors can affect the modulus of elasticity?

The modulus of elasticity can be affected by several factors, including the material's composition, temperature, and level of stress. It may also vary depending on the direction of the applied force and any external factors such as moisture or chemical exposure.

5. How is modulus of elasticity measured?

Modulus of elasticity is typically measured through tensile or compression testing, where a sample of the material is subjected to controlled levels of stress and strain. The resulting data is used to calculate the modulus of elasticity using the stress-strain curve.

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