How Do You Solve a Pulley System Problem with Frictionless Incline?

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In summary, one of the main issues with using pulleys is their tendency to create friction and wear down over time. This can lead to decreased efficiency and potential breakdowns in the system. Additionally, the complexity of pulleys can make them difficult to maintain, requiring specialized knowledge and tools. As such, alternative solutions may be more suitable for certain applications.
  • #1
vu10758
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Two masses are connected as shown at http://viewmorepics.myspace.com/index.cfm?fuseaction=viewImage&friendID=128765607&imageID=1423595691
It is problem 15

I drew my free body diagrams, but I can't figure out the relationship to write for the pulley since the incline is frictionless. I know that angular accleration = (M1*g*sin(theta) - M2*g)R/ (I +M2R^2 +M1*R^2)

How do I get there though? I have to somehow get T1 and T2 out of the problem to write everything in terms of M1,M2,I,R,and theta. However, I am missing an important piece because I don't know the relationship between the forces for the pulley.
 
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  • #2
Write three separate equations: one for M1, one for M2, and one for the pulley. The pulley "knows nothing" about the masses at the other end of the string. All it knows is there are strings with different tensions trying to rotate it in opposite directions.

Express the angular acceleration in terms of the acceleration of the masses. There will then be three unknowns: T1, T2 and acceleration. You can solve the three equations for the three unknowns.
 
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  • #3
Since I know that T1 is greater than T2, wouldn't the pulley have the relationship

T1-T2= Ia, where a is angular acceleration?
 
  • #4
vu10758 said:
Since I know that T1 is greater than T2, wouldn't the pulley have the relationship

T1-T2= Ia, where a is angular acceleration?
Yes. And each mass will have an acceleration that depends in some way on a tension. The angular acceleration of the wheel and the linear acceleration of the masses are all related.
 
  • #5
Thanks, I got it now.
 
  • #6
vu10758 said:
Would you check my work? I got the wrong answer but it seems like my answer is very close

For M1)
x) T1-m1*g*sin(theta)=M1*a
y) N - M1*gcos(theta) <== This is not needed since there is no friction

For M2)

T2+M2*g + M2*a <== This should be
M2*g - T2 = M2*a


Pulley

T1 - T2 = I(alpa) <== This should be
T2 - T1 = I(alpha) It is very important to keep the directions consistent. M1 is moving up the plane, M2 is going down, and the wheel is rotating clockwise.


I know that a is alpha * r <== This is OK

M1*g*sin(theta) + M1*a + M2*a - M2*g = I(alpha)
M1*g*sin(theta) + M1*(r)(alpha) + M2*(r)*alpha - M2*g = I(alpha)
M1*g*sin(theta) -M2*g = I*(alpha) - M1*r(alpha) - M2*r*alpha
alpha = (M1*g*sin(theta) - M2*g)/(I-M1*r - M2*r)

This is wrong though. The correct answer is (M1*g*sin(theta) - M2*g)R/(I + M2*R^2 + M1*R^2)
See the annotations in the quote. Make the corrections and try the Algebra again.
 
  • #7
OlderDan said:
See the annotations in the quote. Make the corrections and try the Algebra again.


Thank you.
 

Related to How Do You Solve a Pulley System Problem with Frictionless Incline?

1. What is a pulley and how does it work?

A pulley is a simple machine that consists of a wheel with a groove around its circumference and a rope or belt running through the groove. It works by changing the direction of force applied to an object, allowing for easier lifting or moving.

2. What are some common problems with pulleys?

Some common problems with pulleys include friction, which can cause the rope or belt to wear out quickly, and misalignment, which can lead to the pulley not working properly.

3. What is another problem with pulleys?

Another problem with pulleys is mechanical advantage. When using multiple pulleys in a system, the mechanical advantage may not be as high as expected due to friction and other factors.

4. How can I reduce friction and prolong the life of my pulleys?

To reduce friction and prolong the life of your pulleys, you can regularly lubricate the wheel and groove with a lubricant such as oil or grease. You can also make sure the rope or belt is properly aligned and not rubbing against any other surfaces.

5. Are there any alternatives to using pulleys?

Yes, there are alternatives to using pulleys such as using gears, levers, or hydraulics. The choice of which mechanism to use depends on the specific application and the desired outcome.

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