Unwinding Spool vs. Standard Block

In summary: The translational kinetic energy for both objects will be the same since they have the same speed and mass.In summary, in this problem involving a block and a spool being pulled with the same tension, they will cross the finish line at the same time due to the same acceleration of the center of mass. However, the spool will have more total kinetic energy due to its spinning and moving motion. This is because the force on the spool does more work as the string unwinds, leading to a greater distance over which the force acts. This extra work goes into rotational kinetic energy. This also means that the translational kinetic energy of both objects will be the same since they have the same speed and mass.
  • #1
ssturb
1
0
Pulling an Unwinding Spool vs. Standard Block

Homework Statement


This problem is done on a frictionless surface
There is a block pulled by a string with tension T.
Next to it, there is a spool with a string wrapped around it and may unwind. It is pulled with the same tension as System A. The spool is standing on its base, so it slides, and doesn't roll.
The question is whether the block or spool will cross the finish line first, which force does more work, and whether the total kinetic energy (trans. + rot.) are equal.


Homework Equations


conceptual

The Attempt at a Solution


They should cross the line at the same time because it shouldn't matter where the force is applied, the object will still accelerate at the same speed. However, the spool should have more total KE because it is spinning and moving when it crosses the finish line, which also means more work is done on it. What I'm confused about is where the extra work comes from. Does the force on the spool do more work because the string is also unwinding, so the force acts over a greater distance than the force acting on the block?
 
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  • #2
ssturb said:
They should cross the line at the same time because it shouldn't matter where the force is applied, the object will still accelerate at the same speed.
Right! The same force produces the same acceleration of the center of mass.
However, the spool should have more total KE because it is spinning and moving when it crosses the finish line, which also means more work is done on it.
Right again.
What I'm confused about is where the extra work comes from. Does the force on the spool do more work because the string is also unwinding, so the force acts over a greater distance than the force acting on the block?
Absolutely right!

Someone pulling the string must do a lot more pulling as the spool unwinds, thus they do more actual work on the spool. That extra work goes into rotational KE.
 
  • #3
Does that mean the translational kinetic energy of the block and spool will be the same?
 
  • #4
bocobuff said:
Does that mean the translational kinetic energy of the block and spool will be the same?
That's right.
 

1. What is the difference between "Unwinding Spool" and "Standard Block"?

The main difference between the two is their design. An unwinding spool is a cylindrical object with a hollow center, while a standard block is a solid rectangular block. The purpose of both is to hold and dispense materials, but their mechanisms differ.

2. Which one is better for dispensing delicate materials?

It ultimately depends on the type of material being dispensed. If the material is fragile and prone to tangling or breaking, then an unwinding spool may be the better option. Its hollow center allows for more gentle and controlled dispensing compared to a standard block, which may be too rough for delicate materials.

3. Is one more cost-effective than the other?

The cost-effectiveness of each option depends on factors such as the type and amount of material being dispensed, as well as the frequency of use. In general, a standard block may be more cost-effective for dispensing larger quantities of materials, while an unwinding spool may be more cost-effective for smaller quantities.

4. Can the same material be dispensed using both options?

Yes, the same material can be dispensed using both an unwinding spool and a standard block. However, certain materials may work better with one option over the other. For example, materials that are prone to tangling may work better with an unwinding spool, while materials that need more force for dispensing may work better with a standard block.

5. Are there any other factors to consider when choosing between the two options?

Besides the material being dispensed, other factors to consider include the speed of dispensing, the space available for the equipment, and the compatibility with other equipment. An unwinding spool may allow for faster dispensing, while a standard block may take up less space. It is also important to ensure that the chosen option is compatible with other equipment in the dispensing process.

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