ally
Junior Member
Cyprus
4 Posts 
Posted  09/20/2008 : 09:24:14

A 40cm diameter 50kg, solid pulley wheel is used to drive a conveyor belt system on a production line. The belt is very light and its mass can be taken as zero. The pulley wheel is accelerated from rest at 2 rad/s^2 for 3 s and then rotated at constant velocity for a further 10s before being decellarted uniformly back to rest in 2s.
1 How far does the belt move during the whole 15s 2 What power is required to accelrate the pulley wheel during the acceleration phase i.e the initial 3 s
For question 1i did the following (If i've went wrong please tell me!)
Multiplied the diameter by pi to get the circumfrence. 1256.64mm Then used the formula theta = (omega0 + omega)t all divided by 2 to get my angular displacement for the accelration in 3 secs.  9 Rads Then used the formula theta = (omega0 + omega)t all divided by 2 to get my angular displacement for the decceleration in 2 secs  6 Rads For the 10 secs of constanst velocity i got 60 rads as the spped was 6 rads per second.
I added all three together and divided by 2pi to get the number of revolutions  11.94 I then multipled the number of revolutions by the circumfrence of the wheel  15000mm (If thats right I'll be amazed!)
I thought i had a fair idea how to do number 2 however After looking through my books I thought I had it all sorted, then i reread a part of the distance learning package, It said that if the mass is not all at the same radius then J=mk^2 where K is the radius of gyration. It then says for any questions given the radius o gyration will be given. Am I right in saying that I have not been given enough information in this question to answer it correctly?


