Help with a statics/dynamics question?

[DrVirz]

Hi all,

I often find myself on this forum when searching google for help on certain topcis, but I only just joined :)

I am having trouble with a homework question. The question states:

If the rod starts from rest in the position shown and a motor drives it for a short time with an angular acceleration of Alpha = (1.5e^t ) rad/s2 , where t is in seconds, determine the magnitude of the angular velocity and the angular displacement of the rod when t = 3s. Locate the point on the rod which has the greatest velocity and acceleration, and compute the magnitudes of the velocity and acceleration of this point when t = 3s. The rod is defined by z = 0.25 sin(Pi y) m, where the argument for the sine is given in radians and y is in meters.

I have attempted the first section, which I think is correct however it seems too simple/odd to me.

Here is a link to the actual question (with diagram), and my working so far.

http://i1374.photobucket.com/albums/ag430/Drvirz/Problem 1_zpsidqrzizz.jpg

https://www.dropbox.com/s/7ibtkysyvxxag64/DSC_0124.JPG?dl=0

If anyone could confirm this is correct/incorrect and provide an insight into the rest of the question that would be fantastic!

Thanks in advance!

Josh

 

[SteamKing]

You should have read the Rules of PF when your joined. There is a HW section which is displayed very prominently at the top of the PF website. I'm moving this thread to the Intro Physics HW forum.

 

[AlephNumbers]

You appear to have integrated correctly to find the angular velocity function. But it says to solve it for when t=3. As for the next part try to find an equation for the angular displacement of the rod with respect to time.

 

[Delta2]

You forgot the constants of integration in ur equations, should be easy to that the first constant for the angular velocity is -3/2, you should also compute the second for the equation of theta.

The point with the maximum velocity and acceleration is that with the maximum z. You should find the y for which z becomes maximum. Then the velocity is $ωz_{max}$ and the acceleration is $Alphaz_{max}$.

 

[AlephNumbers]

Never mind you already did that. Then you should ask yourself which part of the rod has the greatest velocity. The equation v= ωr should help...

 

[DrVirz]

Sorry SteamKing, I will take note for future, and also read the rules.

Just noticed your second comment. I will try and work through the next section and see how i go

 

[DrVirz]

Ok so more or less z=0.25sin(Pi*y) for 0<y<1

So find Z(max) by subbing y-value between 0-1 that will give largest z?

 

[Delta2]

yes but don't forget the constants of integration, the equation for theta becomes a bit different due to the presence of constant of integration in the equation for ω.