- #1
Davidllerenav
- 424
- 14
- Homework Statement
- A spool with thread wound on it, of mass m, rests on a rough horizontal surface. Its moment of inertia relative to its own axis is equal to ##I=\gamma mR^2##, where ##\gamma## is a numerical factor, and ##R## is the outside radius of the spool. The radius of the wound thread layer is equal to ##r##. The spool is pulled without sliding by the thread with constant force F directed at an angle ##\alpha## to the horizontal. Find:
a) the projection of the acceleration vector of the spool axis on the x-axis.
b)the work performed by the force during the first ##t## seconds after the beginning of motio.
- Relevant Equations
- Laws of Newton.
##\tau=lF\sin\theta##
##\tau=l\times F##
##\sum\tau=I\alpha##
I already solved the first part, but according the my book, the answer isn't quite correct. This is what I did.
Finally, I ended up with ##a=\frac{F(r-R\cos\alpha)}{Rm(\gamma+1)}##. But according to my book, the answer is ##a=\frac{F(\cos\alpha-\frac{r}{R})}{m(1+\gamma)}##, what am I doing wrong?
For the second part, I don't know how to find the work done by the force ##F##.