How to avoid the use of a pseudo force

In summary: Newton's third law. In summary, the astronauts cannot exert arbitrary forces on a massless string in space, as their actions must be consistent with Newton's laws of motion.
  • #1
timetraveller123
621
45

Homework Statement


upload_2017-9-17_12-7-10.png
[/B]

upload_2017-9-17_12-6-34.png

Homework Equations


f = ma

The Attempt at a Solution


t1 tension in string connecting Mc
t1 tension in string connecting Ma and Mb
##
m_c:\\
m_c g - T_1 = m_c a_c\\
##
i considered pseudo for acting on masses b and a from a non inertial frame of reference
hence in that frame of reference mass b will go down with aobserved and mass a will go up with a observed
##
m_a,m_b:\\
a_{observed} = \frac{(m_b - m_a)a_c}{m_b + m_a}\\
a_b = a_c - \frac{(m_b - m_a)a_c}{m_b + m_a}\\
a_a = a_c + \frac{(m_b - m_a)a_c}{m_b + m_a}\\

T_2 = m_a a_a = m_b a_b\\

2 T_2 = T_1\\
##
is this correct i have feeling something has gone wrong

but how could i solve without pseudo forces i feel very uncomfortable having to switch frames of references
 
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  • #2
vishnu 73 said:

Homework Statement


View attachment 211246[/B]

View attachment 211245

Homework Equations


f = ma

The Attempt at a Solution


t1 tension in string connecting Mc
t1 tension in string connecting Ma and Mb
##
m_c:\\
m_c g - T_1 = m_c a_c\\
##
i considered pseudo for acting on masses b and a from a non inertial frame of reference
hence in that frame of reference mass b will go down with aobserved and mass a will go up with a observed
##
m_a,m_b:\\
a_{observed} = \frac{(m_b - m_a)a_c}{m_b + m_a}\\
a_b = a_c - \frac{(m_b - m_a)a_c}{m_b + m_a}\\
a_a = a_c + \frac{(m_b - m_a)a_c}{m_b + m_a}\\

T_2 = m_a a_a = m_b a_b\\

2 T_2 = T_1\\
##
is this correct i have feeling something has gone wrong

but how could i solve without pseudo forces i feel very uncomfortable having to switch frames of references
You do not need pseudo force. The "observed acceleration" in the accelerating frame of reference is the relative acceleration with respect to the table (in rest), equal in magnitude and opposite in direction for a and b. The acceleration aa and ab are ac+arelative.
Your work is correct so far, go ahead.
 
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  • #3
no but i used the concept of pseudo force to derive the result for observed acceleration
is there a way to do away with it
 
  • #4
upload_2017-9-17_13-25-8.png

as observed in accelerated frame of reference
 
  • #5
vishnu 73 said:
View attachment 211251
as observed in accelerated frame of reference
Forget accelerating frame of reference. Even then, if the acceleration of block A is arel with respect to the horizontal pulley, that accelerates with ac , the relative acceleration of block B is -arel and aa=ac+arel and ab=ac-arel. Draw the FBD for each block, write the ΣF=ma equations in the rest frame of reference, eliminate the tensions and solve.
 
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  • #6
ehild said:
Forget accelerating frame of reference. Even then, if the acceleration of block A is arel with respect to the horizontal pulley, that accelerates with ac , the relative acceleration of block B is -arel and aa=ac+arel and ab=ac-arel. Draw the FBD for each block, write the ΣF=ma equations in the rest frame of reference, eliminate the tensions and solve.
wow i got the same result without having to use pseudo forces had been having a lot of problems when acceleration was involved but this arel concept cleared it up a lot thanks the rest is just solving the equation i have a few general questions :

lets say there is a massless string in space and two astronauts tug at it one with greater force then there is net force on the string how is that possible ?
 
  • #7
vishnu 73 said:
lets say there is a massless string in space and two astronauts tug at it one with greater force then there is net force on the string how is that possible ?

It's not.

Review Newton's laws.
 
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  • #8
what i am saying is that the force applied by the astronauts can't be controlled by Newtons law ? and are you referring to the third law if so i don't see how that plays a part here please help
 
  • #9
vishnu 73 said:
lets say there is a massless string in space and two astronauts tug at it one with greater force then there is net force on the string how is that possible ?
Can not one astronaut pull the rope with different force than the other.
 
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  • #10
why not it is up to the will of the astronaut
i just can't visualize what does it physically look like
 
  • #11
vishnu 73 said:
why not it is up to the will of the astronaut
i just can't visualize what does it physically look like
How do you exert force on the rope in empty space? It is not enough to want it.
 
  • #12
is it that i will start moving opposite direction?
 
  • #13
vishnu 73 said:
is it that i will start moving opposite direction?
Yes, but how will you start to move when in empty space?
 
  • #14
vishnu 73 said:
What I am saying is that the force applied by the astronauts can't be controlled by Newton's law. And are you referring to the third law? If so, I don't see how that plays a part here. Please help.
vishnu 73 said:
Why not? It is up to the will of the astronaut. I just can't visualize what it physically looks like.
You can't picture it because, as CWatters said, it's impossible. Anything the astronaut can possibly do has to be consistent with Newton's laws. According to your reasoning, you can exert any force on a lightweight object as it's just a matter of will. The third law therefore implies that the object will exert the same magnitude force back on you. Now try to imagine yourself throwing a wad of paper with a 10-N force, about the weight of a kilogram. The paper must exert a 10-N force on your hand. Does that in fact happen?
 
  • #15
vela said:
You can't picture it because, as CWatters said, it's impossible. Anything the astronaut can possibly do has to be consistent with Newton's laws. According to your reasoning, you can exert any force on a lightweight object as it's just a matter of will. The third law therefore implies that the object will exert the same magnitude force back on you. Now try to imagine yourself throwing a wad of paper with a 10-N force, about the weight of a kilogram. The paper must exert a 10-N force on your hand. Does that in fact happen?
yes that happens and i will accelerate backwards but how can i that apply to this situation if the astronaut tugs at the rope with force f backwards then he will accelerated forward same with the other astronaut then what about the other astronaut what is stopping him from applying a different force he would just accelerate with a different acceleration
i am sorry if am not getting what you are saying but it would if you could make it more clear to me
 
  • #16
vishnu 73 said:
yes that happens and i will accelerate backwards.
I guess I should have been clearer. Can you personally actually throw a wad of paper and exert 10 N of force on it? To do so, the wad of paper should push back on your hand with a force that feels like the force you'd need to hold a kilogram mass up. If you can't (or find it very hard to do), why do you suppose this is the case?
 

Related to How to avoid the use of a pseudo force

1. How do pseudo forces arise?

Pseudo forces arise when an observer is in a non-inertial reference frame. This means that the observer is accelerating or rotating, and the objects around them appear to experience a force even though no external force is acting on them.

2. What are some examples of pseudo forces?

Some examples of pseudo forces include centrifugal force, Coriolis force, and the fictitious forces experienced by astronauts in a rotating space station.

3. Why is it important to avoid the use of pseudo forces?

It is important to avoid the use of pseudo forces because they are not real forces and can lead to incorrect conclusions about the behavior of objects. Pseudo forces only appear to exist because of the observer's perspective in a non-inertial reference frame.

4. How can one avoid using pseudo forces?

To avoid using pseudo forces, one can choose to work in an inertial reference frame where no acceleration or rotation is present. Another way is to recognize when a pseudo force is present and to properly account for it in calculations.

5. Are there any situations where pseudo forces are necessary to consider?

Yes, there are situations where pseudo forces are necessary to consider, such as when working in a non-inertial reference frame is unavoidable, such as in a rotating reference frame. Pseudo forces can also be useful in certain situations, such as in the analysis of objects in circular motion.

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