Modeling a center of mass of a thin wire. I am asked to find the moment about the x axis for a thin wire of constant density. This thin wire lies along the curve y=sqrtx and the limits for integration are x=0 and x=2.
Cael Dickerson
Answered question
2022-11-15
Modeling a center of mass of a thin wire I am asked to find the moment about the x axis for a thin wire of constant density. This thin wire lies along the curve and the limits for integration are and . I know from my textbook that the moment about the x axis is: Because this is a thin wire, I know that I need to subdivide the wire into small segments for integration. I have the following for relevant data for each segment: Length: mass: It's the part about the distance of the center of mass to the x axis that I think I'm missing. I have the following:
Therefore, my final integral is:
This particular problem is an odd numbered problem and so I know that I've got it incorrect. Please help me to see where I'm going wrong.
Answer & Explanation
Aiden Villa
Beginner2022-11-16Added 10 answers
Step 1 The center of mass for a wire of constant density making a curve between and is
In the case you describe
The top integral is relatively simple and is equal to
Step 2 The bottom integral may be evaluated by making the substitution to get
Therefore your center of mass is
Kayley Dickson
Beginner2022-11-17Added 3 answers
Step 1 For arc-length integration
Step 2 We can evaluate Numerator and Denominator by parametrization easier with t, max value being