Determining Direction of Acceleration in Pulley Problems

[Balsam]

Homework Statement

In pulley problems, how do you determine the direction of accelleration? My teacher said that acceleration is in the direction of the heavier mass or the steeper incline. Is this true? What if you had two objects of equal mass and only one was on an incline?

Homework Equations

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The Attempt at a Solution

I don't know

 

[haruspex]

Homework Statement

In pulley problems, how do you determine the direction of accelleration? My teacher said that acceleration is in the direction of the heavier mass or the steeper incline. Is this true?

Not really. One could be more massive, but on a gentler incline. Or there may be a pulley system involved which gives mechanical advantage to the lighter mass.
The real answer is that, if there is no friction, it doesn't matter. You can just assume a direction for the acceleration. As long as you are consistent, the equations will be valid. If you guessed wrong, you will get a negative value for the acceleration, which is fine.
With friction it's trickier. You don't know which way the friction will act until you know which way it would move without friction. If it is not obvious which way it would move, solve it ignoring friction first, then add in the friction.

 

[Doc Al]

What if you had two objects of equal mass and only one was on an incline?

You can compare their components of weight along the direction of motion. Whichever is greater will determine the direction of the acceleration.

Even easier: Take a guess as to the direction of the acceleration. Then solve the problem. If your answer is positive, you guessed correct; if negative, you had it backwards.

 

[Kaura]

Just calculate the net force in each direction of the pulley
Make sure to account for friction, gravity, and tension
The side with the most net force should be the side that the system accelerates towards

 

[lonelypancreas]

It's really helpful if you take into account the free-body diagrams of the objects in the system.
Just like how others responded by "guessing" the direction, if your guessed direction is negative then that just means that your direction is towards the opposite true direction of the acceleration.

 

[Balsam]

Just calculate the net force in each direction of the pulley
Make sure to account for friction, gravity, and tension
The side with the most net force should be the side that the system accelerates towards

The way my teacher makes us solve these problems is by calculating the net force of the system as a whole and then to solve for something like accelleration, you do F=ma, using the total mass and total net force. Are you supposed to solve for something like accelleration separately for each mass or do all masses in a

You can compare their components of weight along the direction of motion. Whichever is greater will determine the direction of the acceleration.

Even easier: Take a guess as to the direction of the acceleration. Then solve the problem. If your answer is positive, you guessed correct; if negative, you had it backwards.

Is this because you're supposed to set the direction of accelleration as positive even if its a direction that's commonly labelled as negative(like west)?

 

[Balsam]

You can compare their components of weight along the direction of motion. Whichever is greater will determine the direction of the acceleration.

Even easier: Take a guess as to the direction of the acceleration. Then solve the problem. If your answer is positive, you guessed correct; if negative, you had it backwards.

Won't their components of weight be the same since their weight value is the same?

 

[haruspex]

Is this because you're supposed to set the direction of accelleration as positive even if its a direction that's commonly labelled as negative(like west)?

Not sure what you mean by that.
A good method is to pick a direction as positive for each coordinate. Up and right are the most common choices.
If there is a body that you expect to accelerate to the left, you nevertheless assign it an acceleration variable, a, as its acceleration to the right. In the end you will get a negative value for a.
The benefit of this method is that it helps in getting all the signs right in the equations.

 

[Doc Al]

Is this because you're supposed to set the direction of accelleration as positive even if its a direction that's commonly labelled as negative(like west)?

No (if I understand what you mean). What I mean is: Pick a direction for the acceleration and call its magnitude "a". You can apply your sign convention however you want. When you solve for "a" you'll find out whether you've picked the correct direction by its sign.

Won't their components of weight be the same since their weight value is the same?

No, because one is on an incline: Only a component of its weight acts along the direction of motion.

 

[Balsam]

Not sure what you mean by that.
A good method is to pick a direction as positive for each coordinate. Up and right are the most common choices.
If there is a body that you expect to accelerate to the left, you nevertheless assign it an acceleration variable, a, as its acceleration to the right. In the end you will get a negative value for a.
The benefit of this method is that it helps in getting all the signs right in the equations.

My teacher said to assign the direction of acceleration as positive- so if

is the direction of acceleration, you would make it positive and make

negative, evern though it's usually the other way around​

 

[Balsam]

No (if I understand what you mean). What I mean is: Pick a direction for the acceleration and call its magnitude "a". You can apply your sign convention however you want. When you solve for "a" you'll find out whether you've picked the correct direction by its sign.No, because one is on an incline: Only a component of its weight acts along the direction of motion.

So, if only one was on an incline, the object on the incline would have the greater component of weight? And if both masses are on an incline, the mass on the steeper slope would have the greater component of weight?

 

[haruspex]

So, if only one was on an incline, the object on the incline would have the greater component of weight? And if both masses are on an incline, the mass on the steeper slope would have the greater component of weight?

Yes, but as I posted this assumes a very simple arrangement, one in which if one mass moves the other is sure to move the same distance. If there is a system of pulleys in place this might not be the case.

 

[haruspex]

My teacher said to assign the direction of acceleration as positive- so if

is the direction of acceleration, you would make it positive and make

negative, evern though it's usually the other way around​

I feel there is some text missing in there... maybe some unprintable characters. Anyway, I can't decipher the meaning.

 

[Doc Al]

So, if only one was on an incline, the object on the incline would have the greater component of weight?

Just the opposite.

And if both masses are on an incline, the mass on the steeper slope would have the greater component of weight?

Right.

As far as figuring out the direction of acceleration, take heed of the advice given by haruspex: things can get complicated with systems of pulleys and friction. Nonetheless, you can always assume a direction for acceleration; the equations will tell you if you were correct.

 

[haruspex]

So, if only one was on an incline, the object on the incline would have the greater component of weight?

You may be puzzled that I confirmed that but @Doc Al contradicted me. For some reason, I took you to mean that the other was on the level, but Dr.A is probably right in assuming you meant the other was hanging freely.