- #1
Linus Pauling
- 190
- 0
1. A straight rod has one end at the origin and the other end at the point (L,0) and a linear density given by \lambda=ax^2, where a is a known constant and x is the x coordinate. Since this wire is not uniform, you will have to use integrtation to solve this part. Use M=\int_0^L dm to find the total mass M. Find x_cm for this rod.
2. X_cm = (1/M)Integral(x dm)
3. To obtain M, I did a*Integral(x^2 dx) from 0 to L, obtaining M = (1/3)aL^3
I then did x_cm = (1/M)*a*Integral(x^3) from 0 to L, obtaining:
(3/4)(a^2/L)
Apparently the answer does not depend on a
2. X_cm = (1/M)Integral(x dm)
3. To obtain M, I did a*Integral(x^2 dx) from 0 to L, obtaining M = (1/3)aL^3
I then did x_cm = (1/M)*a*Integral(x^3) from 0 to L, obtaining:
(3/4)(a^2/L)
Apparently the answer does not depend on a