20N Fapp vs 20N mass on a pulley

[dunntastic]

Homework Statement

An unknown mass is hanging from a massless string that runs over a massless, frictionless pulley.

Do the following two scenarios yield the same acceleration? Why?

Scenario 1: a 20N mass is hung on the other end of the string.
Scenario 2: a F_app of 20N is applied downward on the other end of the string.

The Attempt at a Solution

This was on a midterm and the answer is supposedly that they are not the same. Can anyone explain why?

Drawing out the FBDs does seem to support this but it still just doesn't seem right.

 

[cjl]

The reason is because the 20N weight will only exert 20N on the rope if there is no acceleration. The 20N force will exert 20N on the rope all the time.

One good way to envision that they are different, imagine if the mass on the other end of the string was zero. The 20N force would cause infinite acceleration, since it's a force accelerating a massless string and a massless pulley. The 20N weight on the other hand would cause a 1G acceleration, since it would simply be in freefall.

If you fully set up the equations, you should get that the tension of the rope in case 2 is always 20N, while the tension of the rope in case 1 is equal to 20*(1-a/g), where a is the acceleration of the system and g is the local gravitational acceleration. If you solve instead for acceleration, you should get that in case one a = 20N/m (in which m is the unknown mass), but in case two, the acceleration is equal to 20N/(m+20N/g).

(Note: the acceleration given here is for the assumption that the second mass is on a frictionless table. If it is hanging from the other side of the pulley, then the acceleration will be different. The concept, however, still holds)

 

[dunntastic]

Thanks.. that's a little clearer now. Why call a mass a 20N mass when it can only exert 20N sometimes? It sounds to me that the unit of Newtons mean something different when we are talking about masses versus forces?

 

[noleguy33]

Are you sure it's not that one acceleration is negative and the other is positive?

Did you ask your professor?

cjl answer just seems a bit abstract for an intro to physics class.

I'm not sure I understand what part 2 is saying though... what exactly is accelerating?

 

[dunntastic]

It's first semester engineering physics with calculus, so although it is an intro course, high school physics is a prerequisite. If one has absolutely no history with physics, I think there are one or two classes before it.Personally, I just studied a high school physics book and took a placement test to start in this class.

Both the force or the 20N mass would be applying a force downward (pulling the unknown mass upward). It could be accelerating up or down depending on the unknown mass. If the unknown mass were 20N, the system would be static, if it were more, then the unknown mass would be falling, and if it were less, the unknown mass would be accelerating upwards.

It's just hard to imagine that the force is different just because it is applied with a mass as opposed to someone pulling on the rope.

 

[cjl]

Thanks.. that's a little clearer now. Why call a mass a 20N mass when it can only exert 20N sometimes? It sounds to me that the unit of Newtons mean something different when we are talking about masses versus forces?

The mass would be more clearly labeled by its mass rather than its weight, simply because, as you stated here, it will not always exert 20N. On earth, a 20N weight would have a mass of just over 2kg, which is in my opinion a better way to reference it.

However, you definitely need to make sure you understand that in a uniform gravitational field, it will always have 20N of gravitational force acting on it. When it is accelerating however, some force needs to accelerate the mass itself, leaving less to act on other objects. If the object were in freefall, all of the gravitational force would be accelerating the mass itself, so it couldn't be exerting any force on any other object. When it is stationary (or at a constant velocity), none of the force would be accelerating the mass itself, so all of it would go into the other object. Aside from these cases, the force will always be split between accelerating the mass and providing tension on the rope.

(Hopefully this makes sense - I'm trying to be as clear as I can given my state of mind at 2AM)

 

[dunntastic]

in a uniform gravitational field, it will always have 20N of gravitational force acting on it. When it is accelerating however, some force needs to accelerate the mass itself, leaving less to act on other objects. If the object were in freefall, all of the gravitational force would be accelerating the mass itself, so it couldn't be exerting any force on any other object. When it is stationary (or at a constant velocity), none of the force would be accelerating the mass itself, so all of it would go into the other object. Aside from these cases, the force will always be split between accelerating the mass and providing tension on the rope.

Ahhh I get it now. The 20N of a mass is actually the measurement of the gravitational force that acts on the mass, and not some property of the mass (although directly related to it). It then makes sense that a 20N (gravitational) force acting on two masses would have a different acceleration than the same amount of force (applied) acting on only one mass. I just wish the teacher covered that before putting it on the midterm.

 

[cjl]

Yep - it sounds like you've got it now.