How Can We Solve the Connected Bodies Problem with a Resultant Force of 39N?

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Homework Help Overview

The discussion revolves around a physics problem involving connected bodies and the calculation of forces acting on them. The original poster attempts to determine the net force acting on one of the bodies in the system, specifically arriving at a value of 39 Newtons.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss calculating the acceleration of the system and the net force on one body, considering the forces acting on it. There is uncertainty regarding the treatment of friction, with some questioning whether it should be neglected due to a lack of specific values. Others suggest including friction in the calculations and working symbolically rather than numerically.

Discussion Status

The discussion is ongoing, with participants providing guidance on the importance of including friction and working symbolically. There is recognition that the original calculation may be inaccurate, and suggestions have been made to clarify the equations involved.

Contextual Notes

Participants note that the problem states the surface is rough, which raises questions about the treatment of friction in their calculations. There is also mention of the bodies being pushed at a constant velocity, which may influence the approach to the problem.

ayans2495
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Homework Statement
Two boxes are being pushed along a rough carpet surface, as shown below.
Box A has a mass of 30 kg and Box B has a mass of 15 kg. The boxes are being pushed with constant force of 120N.
Calculate the magnitude of the force on block B by block A (F Box B on Box A.)
Relevant Equations
F = ma
1629713449032.png
 
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My solution was to calculate the acceleration of the whole system. Use the obtained value and multiply that by the mass of A to find the net force acting on A. Consider that the net force on A is the sum of the force applied by the person and the force on A by B. And with some more calculations. I obtained a value 39 Newtons. Am I right?
 
Also, I wasn't sure whether or not I was supposed to neglect friction as they said it was on a rough surface, though I believe it would've been impossible to solve the problem if we were to consider friction as there were no given values.
 
ayans2495 said:
My solution was to calculate the acceleration of the whole system. Use the obtained value and multiply that by the mass of A to find the net force acting on A. Consider that the net force on A is the sum of the force applied by the person and the force on A by B. And with some more calculations. I obtained a value 39 Newtons. Am I right?
ayans2495 said:
Also, I wasn't sure whether or not I was supposed to neglect friction as they said it was on a rough surface, though I believe it would've been impossible to solve the problem if we were to consider friction as there were no given values.
It looks like they are being pushed at a constant velocity with a constant force, and yes you should include friction. You don't even need the actual number for the friction coefficient, just assume some value ##\mu_k## and use it in your equations. The answer you got is close, but not correct yet.

Can you show us the equations you get with friction and constant velocity in the problem? It's best if you can post with LaTeX (see the LaTeX Guide link below the Edit window). Thanks.
 
ayans2495 said:
obtained a value 39 Newtons.
As @berkeman notes, that's a bit inaccurate. This will have been a result of plugging in numbers too soon. A much better style is to work entirely symbolically, even putting symbols for given quantities, such as m, M for the two masses. Only plug in numbers at the end.

This has many advantages,
- improves precision
- reduces calculation since often terms cancel
- enables extra ways to spot if and where you have gone wrong (dimensional analysis, special case checks)
- less rework when making corrections
- makes it easier for others to follow your working
...
 

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