Steel Block Rotating On A Steel Table

[TonkaQD4]

A 0.5kg steel block rotates on a steel table while attached to a 1.2meter long hollow tube. Compressed air fed through the tub and ejected from a nozzle on the back of the block exerts thrust force of 4.0N perpendicular to the tube. The maximum tension the tub can withstand without breaking is 50N. If the block starts from rest, how many revolutions does it make before the tube breaks?

u_k = 0.6

Components:

F_y:

n - mg = 0

n= mg

F_x:

F_t - u_kn = ma_x

F_t - u_kmg = ma_x

4.0N - (.6)(.5kg)(9.8m/s^2) = ma_x

4.0N - 2.94N = ma_x

1.06N / .5kg = a_x

a_x = 2.12m/s^2

I found the acceleration of the block, now I need to find the speed at which the tube breaks...

F = ma = (mv^2 / r)

v^2 = (Fr / m)

v = SqRt [(50N)(1.2m) / .5kg ]

v= 10.95m/s

Now do I use a kinematic equation to find distance?

v_f^2 = v_i^2 + 2a(deltaD)

(10.95m/s)^2 = 0 +2(2.12m/s^2) D

D= 10.95 / 4.24

D= 2.58 m

Now this is where I get stuck. If I have done everything correctly up to this point, which I am not sure if I have (correct me if it's wrong), how do I put everything together? What equation do I use?

Any help would be great!

 

[Shooting Star]

You have not said how the tube is lying with respect to the rotating table. A rough diagram or a more vivid description of the set up will help in getting responses.

 

[ogb p]

Thank you.

Based on the information provided, it appears that the block will make approximately 2.58 meters of distance before the tube breaks. However, it is important to note that this is an ideal scenario and does not account for any external factors such as friction or air resistance. In reality, the number of revolutions the block makes before the tube breaks may vary. To accurately determine the number of revolutions, a more complex analysis would be required, taking into account various factors such as the strength of the steel table and the force applied by the compressed air. Additionally, it is important to note that the block may not make a full revolution before the tube breaks, as the force applied by the compressed air may cause the block to move in a linear path rather than a circular one. Overall, while this calculation provides a rough estimate, further analysis and experimentation would be necessary for a more accurate determination of the number of revolutions the block makes before the tube breaks.