Rotation of a drum attached to a spring

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Discussion Overview

The discussion revolves around a homework problem involving the rotation of a drum attached to a spring, focusing on the calculation of maximum angular velocity considering factors such as spring energy, frictional torque, and kinetic energy. The scope includes mathematical reasoning and conceptual clarification related to mechanics.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant equates spring energy to the kinetic energy of the drum, arriving at an angular velocity of 23.4 rad/s, but expresses uncertainty about the next steps.
  • Another participant questions the validity of the calculated angular velocity, suggesting that the peak rate may be reached before the spring becomes slack.
  • There is a discussion about finding the initial tension provided by the spring and the work done by the spring as it contracts.
  • Participants mention the need to account for frictional torque and its effect on the motion of the drum, with calculations suggested for determining the effective frictional force.
  • One participant expresses confusion about the relationship between potential energy of the spring and kinetic energy of the drum, noting the presence of friction as a complicating factor.
  • Several participants request step-by-step guidance, indicating a lack of clarity on how to approach the problem, while others clarify that helpers cannot provide complete solutions but can offer hints and point out errors.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to the problem, with multiple competing views on how to account for spring energy, friction, and the relationship between potential and kinetic energy. The discussion remains unresolved.

Contextual Notes

Limitations include potential misunderstandings of the problem setup, the need for clearer definitions of variables, and unresolved mathematical steps regarding the energy transformations involved.

Datta108
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Homework Statement


Rotation of a small drum of mass moment of inertia 0.44kg.m^2 and with frictional resistance torque 0.3 N.m is initiated by a string wound around its 20 mm diameter shaft and attached to a stretched spring, as shown in the figure. If the spring, which has a stiffness 2N/mm is initially stretched by 120 mm before the drum is released from rest, determine the maximum angular velocity, in rpm, attained by the drum.

Homework Equations


Tnet = Iα
SE = 1/2 kx^2
KE of drum = 1/2Iw^2

The Attempt at a Solution


The spring energy provided by the stretched spring is given to the drum and converted to the kinetic energy of the drum. Equating these two gives w = 23.4 rad/s^2. I don't know how to proceed from here. I believe we have to find the T provided by the spring. Then, the first equation can be used to find the difference in T and therefore alpha can be found. From this v can also be found. However, I am stuck at finding T provided by spring.

Any help (ASAP) will be greatly appreciated.

Many Thanks!
 
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Datta108 said:
Equating these two gives w = 23.4 rad/s^2
That is not going to help since the peak rate isprobably reached before the spring becomes slack.
Datta108 said:
stuck at finding T provided by spring
There is no difficulty finding the initial tension, is there?
Consider when the spring has contracted by a distance x from its initial stretch. What work has been done by the spring? What is the KE of the drum?
 
Using the frictional torque and the radius, you can find an effective "frictional force" acting at the edge.
 
haruspex said:
That is not going to help since the peak rate isprobably reached before the spring becomes slack.

There is no difficulty finding the initial tension, is there?
Consider when the spring has contracted by a distance x from its initial stretch. What work has been done by the spring? What is the KE of the drum?

Sorry, did you mean torque?

Work done by the spring would be 1/2kx^2.
Won't the KE of the drum equal the SE of the spring?Sorry if I am asking stupid questions here, but my tutor did not go over such problems in detail.
(This is NOT to complete my homework by the way. I am studying for an exam that's coming up)
 
scottdave said:
Using the frictional torque and the radius, you can find an effective "frictional force" acting at the edge.
Do you mean 0.3 N.m * 0.010 m?
 
Look at the units. You want to divide (0.3 N*m) / (0.01 m) to get 30 Newtons of friction, which works against motion of the drum (so it is in opposite direction of spring force).
 
Datta108 said:
Work done by the spring would be 1/2kx^2.
No. It started with extension L (=0.12m) and I defined x as the reduction in extension, so:
- what PE did the spring start with? (Use L, not the numerical value.)
- what PE does it still have?
- what work has it done?
Datta108 said:
Won't the KE of the drum equal the SE of the spring?
No, there s friction. How much work has been done against that?
 
haruspex said:
No. It started with extension L (=0.12m) and I defined x as the reduction in extension, so:
- what PE did the spring start with? (Use L, not the numerical value.)
- what PE does it still have?
- what work has it done?

No, there s friction. How much work has been done against that?
Sorry, I am not able to think about this problem. Could you please give me a step by step method for this question?
I have a mechanics exam tomorrow. Thank you.
 
Datta108 said:
Sorry, I am not able to think about this problem. Could you please give me a step by step method for this question?
I have a mechanics exam tomorrow. Thank you.
Sorry, helpers are not permitted to provide step by step solutions for homework problems. They can offer hints and point out errors in work you've shown, or offer suggestions concepts to think about or try.
 
  • #10
gneill said:
Sorry, helpers are not permitted to provide step by step solutions for homework problems. They can offer hints and point out errors in work you've shown, or offer suggestions concepts to think about or try.
Sorry, I was not aware of this. Thank you all!
 

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