Steel Block Rotating On A Steel Table

In summary, a 0.5kg steel block is attached to a 1.2meter long hollow tube, which is rotating on a steel table. Compressed air is fed through the tube and ejected from a nozzle on the back of the block, exerting a thrust force of 4.0N perpendicular to the tube. The maximum tension the tube can withstand without breaking is 50N. Using the given information, the acceleration of the block is calculated to be 2.12m/s^2. The speed at which the tube breaks is found to be 10.95m/s. However, the distance the block travels before the tube breaks is unclear without more information about the set up. It is suggested to provide
  • #1
TonkaQD4
56
0
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!
 
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  • #2
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.
 
  • #3
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.
 

FAQ: Steel Block Rotating On A Steel Table

What is the purpose of studying a steel block rotating on a steel table?

Studying the motion of a steel block rotating on a steel table can help us understand the principles of rotational motion, friction, and energy conservation. This can have practical applications in engineering and design.

How does the mass of the steel block affect its rotation on the steel table?

The mass of the steel block directly affects its rotational inertia, which is the resistance to changes in rotational motion. A heavier block will have a larger rotational inertia, making it more difficult to change its rotation.

What factors affect the friction between the steel block and steel table?

The friction between the steel block and steel table is affected by the materials of both surfaces, the force pressing the block onto the table, and any lubricants or contaminants present. The roughness and temperature of the surfaces can also play a role.

How does the shape of the steel block affect its rotation on the steel table?

The shape of the steel block can affect its rotational motion by changing its distribution of mass. A block with a more elongated shape will have a different rotational inertia than a block with a more compact shape.

What are some real-world applications of studying a steel block rotating on a steel table?

Understanding the principles of rotational motion and friction can have practical applications in designing machinery, improving the efficiency of machines, and predicting the behavior of rotating objects in various industries such as manufacturing, transportation, and aerospace.

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