Solving Belt Around Pulleys Homework: 0.6 m/s, 1.44 m/s2, 1.56 m/s2

[pconn5]

Homework Statement

A belt passes over two pulleys O1 (radius R1= 0.4 m) and O2 (radius R2 = 0.6 m) as shown, and points A and B are on the rim of the pulleys. The normal acceleration at A is 0.9 m/s2 and the angular acceleration of pulley O1 is 3.6 rad/s2. Find (a) the belt velocity υb, (b) the belt acceleration ab, and (c) the acceleration of B.

Homework Equations

a n= v^2/R
angular acceleration and velocity equations

The Attempt at a Solution

I got a by using a n=v^2/R... so .9 = v^2/.4, v = .6 which is correct. I do not know how to go about finding the other values at all.

answers: (a) 0.6 m/s (b) 1.44 m/s2 (c) 1.56 m/s2

 

[CaptainEvil]

Draw free body diagrams for your two pulleys, label all the forces acting on them, including torques, and use Newtons second law to derive equations that can help you solve for your unknowns. You may have to look up the moment of inertia of a pulley (a cylinder I suppose?)

 

[alexshaf]

How's VTech? haha, I just finished it, and I'll post now:

so we have:

r1=.4 m
r2=.6 m
Ana= .9 m/s^2 (this is normal acceleration for point A)
alpha1= 3.6 rad/s^2 (this is angular acceleration for O1)

In order to find Belt Velocity we...

Ana=(wa^2)(r1) => wa=sqrt((Ana)/r1)) = 1.5 => v=wr=(1.5)(.4)=.6m/s

In order to find Belt Acceleration we...

at (tangential acceleration) = (alpha1)(r1) = 1.44 m/s^2

In order to find acceleration of B:

we know that at above =1.44m/s^2

we can solve for Anb=(v^2)/(r2)=(.6^2)/(.6)=.6
so TOTAL acceleration of aT

aT=sqrt((at^2)+(Anb^2))=1.56 m/s^2

Sorry about the sloppy notation :-/