mms05 is right, the displacement on a curved ramp would be different than that on a straight ramp, but, in this particular problem you can use a different approach , just like Teegvin said, in order to calculate work.
W = - (Uf - Ui)
where Uf is the final potential energy and Ui is...
Ok, i see what you mean. But is there any way to do the problem with this ecuation?
m(-\rho \dot{\theta^2} \hat{\rho} + \rho \ddot{\theta} \hat{\theta}) = N \hat{\rho} + T \hat{\theta} - mg\sin(\theta)\hat{\rho} - mg\cos(\theta)\hat{\theta}
i mean, imposing the conditions in it...
work is the difference between the final and initial potential energy of the system (although this only applies if the force is conservative), that's why you were getting a negative sign.
Sorry, i made a mistake
a_0 = R\ddot{\theta} \Longleftrightarrow a_0 = R\frac{d\dot{\theta}}{d\theta} \frac{d\theta}{dt}
\Longleftrightarrow a_0d\theta = R\dot{\theta}d\dot{\theta}
if we now integrate the left side between \theta = 0 and \theta = \theta_1 and the right side between...
Sorry, i had a final exam yesterday, so i checked your answer but i planned on responding today.
i have a different approach
a_0 = R\ddot{\theta} \Longleftrightarrow a_0 = R\frac{d\dot{\theta}}{d\theta} \frac{d\theta}{dt}
\Longleftrightarrow a_0d\theta = R\dot{\theta}d\dot{\theta}...
I'm sorry, you're absolutely right. I wasn't thinking on the meaning of the ecuations, just trying to solve them and overlooked the fact that \rho \dot{\theta^2} is \frac{v_t}{r}. v_t being tangential velocity.
So, the ecuation for \hat{\rho} would be:
m(-\rho \dot{\theta^2}) = N...
Are you sure? because a0 will generate an acceleration in \hat{\theta} and the radial component of the wight generates the acceleration in \hat{\rho}
i know the condition for the first question is that the normal (N) becomes 0and for the second one that the tension becomes 0, but in both...
sorry, here goes an image of the system
http://img220.imageshack.us/my.php?image=dibujo2lr.jpg
jajajaja, it doesn't look too good, but you'll get the picture
Hi, I'm from Chile, so i had to translate the problem from spanish and my english ain't that good so if you don't understand something, please tell me.
A particle of mass m is initially at rest at the edge of a horizontal semicilinder of radius R (theta (t=0)=0). The particle is tied to an...