Conservation of energy problem

In summary, a metal disk with a mass of 250g and a radius of 12cm is free to rotate about a frictionless vertical axle with negligible mass and a radius of 2cm. A string wrapped around the axle is connected to a hanging 85g mass and a dime (2g) sits on the edge of the disk with a static coefficient of friction of 0.250. The 85g mass is released and begins to fall, and the problem is to determine how far it will fall before the dime slides off the disk. The maximum rotational speed of the disk before the dime starts to slide can be found by considering that static friction provides the centripetal force. Then, using conservation
  • #1
kornwestheim
7
0
Okay here is the problem.
A metal disk ( mass 250g , radius12 cm) is free to rotate about frictionless vertical axle through its center. The axle itself has negligible mass and a radius of 2 cm. A string wrapped around the axle passes over an ideal pulley to a hanging 85 g mass. A dime ( mass 2 g) sits on the edge of a metal disk. The statis coefficient of friction between the dime and the metal disk is u= 0.250.
The 85g mass is released from rest and beginns to fall. How far does it fall before the dime slides of the disk?

I have a hard time to setup the equation.
Any hint or help is appriciated
 
Physics news on Phys.org
  • #2
This is what I tried so far

Ui+Ki=Uf+Kf
mgh= (1/4 M(R squared) +m(r squared) +1/2m(V squared) +

I am not sure if this is complete since I can’t figure out if the dime has also final potential energy and also how to add the friction in this
I know for dime that n=mg and that Ffr= u*mg but how should I know the h height when the system starts to move.
If I try to calculate the angular velocity I am still having one unknown ( h) but even if I would know I am not sure how to relate the angular velocity with Ffr.
If I try via torque I don't have the angular accel ?
 
  • #3
Is there anyone to help me on this one ??
 
  • #4
Start by figuring out the maximum rotational speed that the disk can have before the dime starts to slide off. Hint: Consider that static friction is providing the centripetal force.

Once you have that, then use conservation of mechanical energy to determine how far the falling mass drops.
 
  • #5
Thanks Doc Al,

Can you check work I did to see if I did it right
 

Attachments

  • Forces on dime.doc
    19.5 KB · Views: 168
  • #6
kornwestheim said:
Can you check work I did to see if I did it right
Some comments. First, you seem to confuse tangential acceleration with radial acceleration. Second, you use the same symbol (m) to represent both the 85g and 2g masses. Third, you stopped too soon: Your final answer should not be in terms of v or [itex]\omega[/itex]. (What's the relationship between them?)
 
  • #7
Doc Al said:
Some comments. First, you seem to confuse tangential acceleration with radial acceleration.
Second, you use the same symbol (m) to represent both the 85g and 2g masses. Third, you stopped too soon: Your final answer should not be in terms of v or [itex]\omega[/itex]. (What's the relationship between them?)

I am not quite sure what do you mean with confusion of radial and tangetinal acceleration. I know I acctually did not need the radial accel., but I needed the tangential to find the angular velocity ( ar= r *omega ^2) This is was actually only part I was not quite sure about. Is this relationship cvorrect?
And, Yes I was a little bit careless with subscripts of masses.
The relationship between them them is v= r*omega.
 
  • #8
kornwestheim said:
I am not quite sure what do you mean with confusion of radial and tangetinal acceleration. I know I acctually did not need the radial accel., but I needed the tangential to find the angular velocity ( ar= r *omega ^2) This is was actually only part I was not quite sure about. Is this relationship cvorrect?
This is just my point. You need radial acceleration, not tangential. But, yes, radial acceleration is given by [itex]a_r = \omega^2 r[/itex].

The relationship between them them is v= r*omega.
Yes--just be sure to use the correct radius.
 
  • #9
Doc Al said:
This is just my point. You need radial acceleration, not tangential. But, yes, radial acceleration is given by [itex]a_r = \omega^2 r[/itex].


Yes--just be sure to use the correct radius.

Thanks Doc Al
 

1. What is the conservation of energy problem?

The conservation of energy problem is a fundamental principle in physics that states energy cannot be created or destroyed, only transferred or converted from one form to another.

2. Why is the conservation of energy problem important?

The conservation of energy problem is important because it helps us understand how energy behaves in various systems and allows us to make accurate predictions about the behavior of physical systems.

3. How is the conservation of energy problem applied in real life?

The conservation of energy problem is applied in various real-life scenarios, such as in the design of energy-efficient buildings, the development of renewable energy sources, and the understanding of natural processes like photosynthesis and the water cycle.

4. Can the conservation of energy problem be violated?

No, the conservation of energy problem is a fundamental law of physics and has been extensively tested and proven to hold true in all physical systems. Any apparent violations are due to measurement errors or incomplete understanding of the system.

5. Are there any exceptions to the conservation of energy problem?

There are no known exceptions to the conservation of energy problem. However, in quantum mechanics, there are phenomena such as quantum tunneling and virtual particles that may seem to violate the conservation of energy, but these are still in accordance with the principles of energy conservation on a larger scale.

Similar threads

  • Introductory Physics Homework Help
2
Replies
44
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
935
  • Introductory Physics Homework Help
2
Replies
55
Views
1K
Replies
10
Views
313
  • Introductory Physics Homework Help
Replies
24
Views
891
  • Introductory Physics Homework Help
Replies
3
Views
967
  • Introductory Physics Homework Help
Replies
6
Views
990
  • Introductory Physics Homework Help
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
30
Views
1K
Replies
41
Views
2K
Back
Top