A rod is 2.40 m long and has a diameter of 2.50 mm. A force of 2000 N is applied to the end to stretch the rod by 1.40 mm. What is the tensile modulus for this rod?
To find the tensile modulus of the rod, we need to use Hooke's Law, which states that the strain produced in a material is directly proportional to the stress applied to it. The formula for Hooke's Law is:
Stress = Young's modulus × Strain
In this case, the strain is the change in length divided by the original length, and the stress is the force applied divided by the cross-sectional area of the rod.
1. First, let's calculate the cross-sectional area of the rod using the formula for the area of a circle:
Area = π × (Radius)^2
Since the diameter of the rod is given as 2.50 mm, we need to divide it by 2 to find the radius:
Radius = 2.50 mm / 2 = 1.25 mm = 0.00125 m
Therefore, the cross-sectional area is:
Area = π × (0.00125 m)^2
2. Next, let's calculate the strain using the given values:
Strain = Change in length / Original length
Change in length = 1.40 mm = 0.0014 m
Original length = 2.40 m
Thus, the strain is:
Strain = 0.0014 m / 2.40 m
3. Now, we can calculate the stress:
Stress = Force / Area
Force = 2000 N (Given)
Substituting the values into the equation, we get:
Stress = 2000 N / Area
4. Finally, let's rearrange the equation for Hooke's Law to solve for Young's modulus (tensile modulus):
Young's modulus = Stress / Strain
Substituting the values we calculated earlier, we have:
Young's modulus = (2000 N / Area) / (0.0014 m / 2.40 m)
Now, we can calculate the tensile modulus of the rod.