Two mass hanging on a pulley

[Vay]

A pulley is attached to the ceiling. Two masses hang from the pulley, one on either side. Mass(1) is smaller than mass(2), all in terms of kg(kilograms). We take downward as positive direction. The cords attaching the masses are mass-less and does not slip on the pulley.

 

The question is to find the tangential force on the pulley. The book says the net tangential force on the pulley is (tension(2) - Tension(1)), where the unit of force is N(newtons). I thought the net tangential force acting on the pulley is (Mass(2))(a)-(Mass(1))(a). Anyone know why I am wrong?

Edited May 21, 2013 by Vay

[John Cuthber]

What are the units of mass and what are the units of force?

[Vay]

What are the units of mass and what are the units of force?

 

Force is in newtons and mass is in kilograms. The units shouldn't be important to the question; it's more of a conceptual problem. Why do we use tension instead of the force of the blocks. I thought if someone was pulling a cord attached to a pulley, the tangential force would be the force of the hand pulling it, right? But the book says it's the tension force. It also turns out the tension forces calculated for the two mass-less cords are not the same as the force of the two blocks. The book doesn't mention the mass of the pulley, that might be why, but I am still trying to figure out the link.

 

The way I see it is, the difference between the forces acting on the block, is the same amount of force lost in turning the pulley. This force difference between the two blocks gives the pulley the turn, and is the tangential force on the pulley, am I right?

 

Edit: My prediction is wrong since Mass(2) and Mass(1) both have the same same magnitude of acceleration, but in different directions, so that means their forces are already different before losing some force into turning the pulley.

 

I think I solved the problem: The force acting on the block is not the same as the tension force. This is because the block is left to freely fall, meaning the force on the block is greater than the tension force. If the tension force was (Mass(2))(a), then the Mass(2) would not be falling. Force Mass(2)(a) is decreased from Mass(2)(g) because of the inertia of the pulley and the inertia of Mass(1). This reduction of force means that there is a force pulling in the opposite direction of Mass(2), which is the upward force of Mass(2)(g)-Mass(2)(a). Given that Mass(2)(a) > Mass(2)(g)-Mass(2)(a) because the upward force on Mass(2) does not stop Mass(2) from falling, means that the tension in the cord is Mass(2)(g)-Mass(2)(a), and since the cord is in contact with the pulley, the tangential force is the tension force, which is Mass(2)(g)-Mass(2)(a). Without the tension force, Mass(2) will fall freely.

 

TLDR: The pulley is not actually supporting a force of Mass(2)(a), because if that was so Mass(2) would not be falling. Instead, the pulley is supporting, with the help of Mass(1) weighing in on the other cord, a different force, a smaller force, which is the tension force in the cord. This concept is still not crystal clear in my mind and so I will probably forget it during the finals...

Edited May 22, 2013 by Vay

[MigL]

The units are important to the question. What John is trying to get at is called dimensional analysis. You cannot have different units on either side of an 'equal' sign. You had force (units)=mass(units), which is nonsensical. This is an easy way to check your results.

[John Cuthber]

The units are important for another reason.

Imagine you take your pulley to the moon.

Same masses, but different forces.

[SplitInfinity]

A pulley is attached to the ceiling. Two masses hang from the pulley, one on either side. Mass(1) is smaller than mass(2), all in terms of kg(kilograms). We take downward as positive direction. The cords attaching the masses are mass-less and does not slip on the pulley.

 

The question is to find the tangential force on the pulley. The book says the net tangential force on the pulley is (tension(2) - Tension(1)), where the unit of force is N(newtons). I thought the net tangential force acting on the pulley is (Mass(2))(a)-(Mass(1))(a). Anyone know why I am wrong?

 

Vay...you do know that if the cords are Mass-less then there cannot be tension on the pulley...right?

 

The whole purpose of this question is to show how there will be different tension based forces upon a pulley based upon the mass on either side of the pulley. Since Gravity is NOT A FORCE but in fact is an EFFECT regardless of what you or anyone else has been taught...we label Gravity as the Weak Force as a way to make it easy for people to understand.

 

Force is defined as the INTERACTIONS OF QUANTUM FIELDS....This is true for Magnetism or Electromagnetism...as Quantum Particle/Wave Forms...in this case...Electron Orbital Fields....are the Quantum Field Interaction as Elements that can take on additional Electrons in their Orbital Electron Fields....will do so and in the case of EM...adding such Electrons by running an electric charge into a large metal disc on the end of a crane will allow the disc to grab on by EM to the steel roof of a car as the electrons flow into the empty orbits of the Iron based Steel and thus form an EM attraction bond.

 

That is an Electromagnetic FORCE.

 

If I were to hit a baseball with a bat I am forcing the bat into motion my Kinetic Energy and when the bat hits the ball and the ball shoots away...Hopefully out of the park! LOL! The Kinetic Energy Force of the Moving Bat...F=MA...contacts the Ball thus transferring that Kinetic Energy by the means of the Quantum Field Interaction as the Electron Orbital Fields surrounding the Atoms Nucleus' that make up the bat and ball repel each other as they are both negatively charged.

 

The Bat and Ball actually NEVER TOUCH EACH OTHER AND NEVER COME IN CONTACT WITH EACH OTHER. The Electron Orbital Fields or the Quantum Fields interact with each other and repel one another causing the particles of Mass...ie...Protons and Neutrons....that give the ball and bat weight and substance....never come into contact. The funny thing though is that THE PROTONS AND NEUTRONS ARE COMPLETELY COMPRISED OF QUANTUM PARTICLE/WAVE FORMS and at their very smallest level of existence are completely made of ENERGY.

 

So anything that is a FORCE...is specific to Quantum Field Interaction. GRAVITY is not specific to Quantum Field Interaction thus GRAVITY IS NOT A FORCE. We call it one to make it easier to understand but in reality....GRAVITY IS SPACE/TIME DIMENSIONALITY and specifically...AN EXPRESSION OF ONE DIMENSIONALITY in our Multi-Dimensional Universal Space/Time.

 

So...this question has two objects of mass...one of greater mass than the other...and since the quantity of Mass is not given...and not to be a pain but you should have stated...Mass 1 has less mass than Mass 2. The way you said it...Mass 1 is smaller than Mass 2...means that one object is SMALLER IN SIZE...it does not tell us it is lessor in the amount of Mass. This is important when talking about a pulley as if one object is 100 cubic feet and the other is 10 cubic feet and they are hanging by a cord connected to a pulley...distribution of Mass can play havoc in a system of pulleys.

 

Still...we have no idea of the comparative amounts of mass nor do we know the cord length nor do we know the pulleys configuration and even the weight of the cord...how the cord is attached to the objects...how in-line the hanging objects are due to distribution of mass...and in the REAL WORLD....WIND, TEMP, ATM. PRESSURE...ETC...ETC...

 

So...there we are.

 

Split Infinity

[imatfaal]

!

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