Circular motion

[rakuenso]

Here's the problem:

 

A 500g steel block rotates on a steel table while attached to a 1.2m long hollow tube. Compressed air fed through the tube and ejected from a nozzle on the back of the block exerts a thrust force of 4.0 N perpendicular to the tube. The maximum tension the tube can withstand without breaking is 50N. If the block starts from rest, how man revolutions does it make before the tube breaks.

 

 

Now back of my text book tells me its 3.75 revolutions

 

 

But here's my solution:

 

I approached to this problem via the rtz-axis,

 

(Fnet)r = Tension of hollow tube = mass*w^2*radius (w, for angular velocity

(Fnet)t = Force of thrust = mass*(acceleration in the t direction)

 

 

So knowing all this,

 

First I solved for w (angular velocity):

 

50 N=0.5kg(w^2)(1.2)

w(final)=9.129 rad/sec

 

Then I solved for acceleration in the t direction:

 

4N=0.5kg(At)

At=8m/s^2

 

 

 

Finally I used the formulas for non-uniform circular motion:

 

theta(final)=theta(initial) + w(initial)(time) + (acceleration t)/(2r) * (time^2)

 

and

 

w(final) = w(initial) + (acceleration t)/(radius) * (time)

 

 

Ok I plug everything into the second equation:

 

9.129 = 0 (because object starts at rest) + 8/(1.2) * time

time = 1.369

 

Then I plug it back into the first equation

theta(final)= 0 (once again because objects starts at rest) + 0 + 8/(2.4) (1.369^2) = ~6.25 rad

 

6.25 rad = ~.995 revolutions...

[swansont]

I agree with your analysis. It makes just less than 1 revolution.

[rakuenso]

i found out my error, I neglected kinetic friction... (although i'm not sure why its kinetic and not static and kinetic since the object starts from rest)

[swansont]

i found out my error, I neglected kinetic friction... (although i'm not sure why its kinetic and not static and kinetic since the object starts from rest)

 

Static only applies at the very start of the problem - once it's moving, you need only consider kinetic friction. As long as the static friction is less than 4.0 N, you can ignore it.