Two Objects Connected by a Pulley: Solving for m1

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In summary, the problem involves two objects connected by a string over an elevated pulley and starting to slide with friction present. The question asks for the position of the first mass (m1) when the system comes to rest with a given height (h) and friction coefficient (μ=0). The problem is unclear and open to interpretation, as it is not specified whether μ=0 means no friction or to ignore friction. One approach could be to find the equilibrium position where the normal force exerted by the table on m1 becomes zero, assuming the pulley has zero radius. Another possibility is that the system will continue to move until the point of force application is directly under the pulley. The problem lacks clarity and could benefit from
  • #1
JWSiow
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Homework Statement


Two objects with masses m1 of 10kg and m2 of 2kg are connected with a string over an elevated pulley as shown and start to slide in the presence of friction.

http://www.freeimagehosting.net/uploads/06f5aea24d.jpg

If h=10cm and [tex]\mu[/tex]=0, where is m1 when the system comes to rest


Homework Equations





The Attempt at a Solution


I have absolutely no idea with this one...
 
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  • #2
Do you mean in the presence of friction μ = 0?
 
  • #3
This problem requires some interpretation. What does μ = 0 mean? Can it mean no friction? Yet the problem says "in the presence of friction." It might mean "don't worry about friction as a force acting on the mass when the mass comes to rest", but I am not sure. Have you posted the exact wording of the problem as given to you?
 
  • #4
Yep, that's one of the things that confused me. I assumed it meant ignore friction..
 
  • #5
The question "where is m1 when the system comes to rest" is also a bit unclear. Suppose you could find angle θ. How would that help you determine where the mass is from, say, the edge of the table? The best you can do is to assume that the pulley has zero radius and find the distance of the mass to the center of the pulley.

My guess for approaching this (not so well-designed) problem is to say that the equilibrium position is where the normal force exerted by the table on m1 becomes zero. You can find θ from this condition.
 
  • #6
JWSiow said:
Yep, that's one of the things that confused me. I assumed it meant ignore friction..
It is stange, but we have no choice - we have to respect facts :smile:. There are three forces action on the m1: gravity, table reaction and string tension.

IF there is no friction there is unbalanced horizontal component of string tension. It is non-zero force until theta angle lower than 90 deg. And I can't see anything to balance this force.

This mean that system moves until point of force application locate preciselly under pulley?

Like blue one on the picture below

http://www.freeimagehosting.net/uploads/c78bf6258f.jpg

regards
Bartek
ps
But it is confusion me too.
 
  • #7
Thanks anyway :) Any answer's better than none! Hopefully they don't put anything weird like that in my exam!
 

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

A pulley is a simple machine that is used to change the direction of a force. It consists of a grooved wheel and a rope or cable that runs through the groove. When a force is applied to one end of the rope, it causes the wheel to rotate, allowing for the transfer of force to another object.

2. How are two objects connected by a pulley?

In a simple pulley system, two objects are connected by a rope or cable that runs through the pulley. One object is attached to one end of the rope, and the other object is attached to the other end of the rope. As the rope moves through the pulley, the objects will move in opposite directions.

3. What is the equation for solving for m1 in a two object pulley system?

The equation for solving for m1 in a two object pulley system is: m1 = (m2 * d2) / d1, where m1 is the mass of one object, m2 is the mass of the other object, d1 is the distance between the pulley and the object with mass m1, and d2 is the distance between the pulley and the object with mass m2.

4. How do you determine the direction of motion for each object in a two object pulley system?

In a two object pulley system, the direction of motion for each object is determined by the direction of the force applied to the rope. If the force is applied downwards, the object attached to that end of the rope will move downwards, and the other object will move upwards. If the force is applied upwards, the opposite will happen.

5. What are some real-life applications of a two object pulley system?

A two object pulley system is commonly used in many different industries, such as construction, transportation, and manufacturing. Some examples of real-life applications include elevators, cranes, and conveyor belts. Pulleys are also used in exercise equipment, such as weight machines and resistance bands.

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