How to Find the Force Needed to Reduce Acceleration by 50% in Atwood Setup

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Homework Help Overview

The discussion revolves around an Atwood machine setup where an additional force is applied to one of the masses, and the goal is to determine the force required to reduce the system's acceleration by 50%. The participants are working with the equations of motion for two masses, m1 and m2, and exploring how the introduction of this force affects the system's dynamics.

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  • Mixed

Approaches and Questions Raised

  • Participants are attempting to derive equations based on the forces acting on the masses and are questioning how to incorporate the additional force into their existing equations. Some are unsure about the relationship between the forces and the new acceleration.

Discussion Status

There is ongoing exploration of the equations needed to solve for the force. Some participants have provided partial equations and values, while others are seeking clarification on how to adjust their calculations with the new force included. Multiple interpretations of the problem setup are being discussed.

Contextual Notes

Participants are working under the constraint of a specific acceleration value that is half of the original, and there is confusion regarding the treatment of mass versus force in their equations. The problem context emphasizes the need to adjust their approach based on the additional force without changing the mass of m1.

parwana
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Suppose that in the same Atwood setup another string is attached to the bottom of m1 and a constant force f is applied, retarding the upward motion of m1. If m1 = 4.00 kg and m2 = 8.00 kg, what value of f will reduce the acceleration of the system by 50%?

Now I got the equations for these two as

for M1= T-4g= 4a
for M2= 8g-T= 8a

I got a as 3.266

I got T as 52.264

But I can't get the answer to the asked question. Please HELP me solve this.
 
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Now you have an additional force acting on m1 and a given acceleration. Rewrite your equations accordingly and solve for that force.
 
I don't know how to do that, please help
 
How did you get those first equations? It's the same analysis, only now there is an additional force acting on m1.
 
So is it going to be

T-(4+x)g= (4+x)a

Please help me, I am so fed up of trying to get this right.
 
please help, I am so fed up of this problem.
 
parwana said:
So is it going to be

T-(4+x)g= (4+x)a

Please help me, I am so fed up of trying to get this right.
No. What you have written assumes mass is being added to m1. No mass is being added. There is an additional force acting, but no additional mass. Also, you have been given the acceleration as half what it was without the additional force, so (a) is now known.
 
I don't understand still, can you write it in a equation like I did?
 
So will it be

T-4g-F= 4(.5a)

In that case I got F= 19.596
 
  • #10
parwana said:
So will it be

T-4g-F= 4(.5a)

In that case I got F= 19.596
Did you use the old T, or caclulate the new T? The old T will not work.
 
  • #11
Try this. Take your original equations:
parwana said:
for M1= T-4g= 4a
for M2= 8g-T= 8a

I got a as 3.266
Now add the new force F on M1. The equations become:
(for M1) T -4g -F = 4a
(for M2) 8g - T = 8a

You have two unknowns: T and F. Solve for F. (This time around "a" is not an unknown--it's given as 3.266/2 m/s^2.)
 
  • #12
thank u so much
 

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