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

In summary, by working symbolically and using known values for the quantities, you can improve your accuracy and reduce the amount of calculation you need to do.
  • #1
ayans2495
58
2
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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  • #2
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?
 
  • #3
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.
 
  • #4
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.
 
  • #5
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
...
 

1. What is the "connected bodies problem" and why is it important to solve?

The connected bodies problem refers to a situation where multiple objects are connected together and are experiencing a force acting on them. It is important to solve because understanding how forces act on connected bodies is crucial in many real-world scenarios, such as designing structures or analyzing the motion of objects.

2. How can we determine the resultant force acting on connected bodies?

The resultant force can be determined by adding together all the individual forces acting on the connected bodies. This can be done by using vector addition, where the magnitude and direction of each force are taken into account.

3. What is the significance of a resultant force of 39N in the connected bodies problem?

A resultant force of 39N means that the total force acting on the connected bodies is 39N, and it has a specific direction. This information can be used to calculate the acceleration of the connected bodies and predict their motion.

4. How can we solve the connected bodies problem with a resultant force of 39N?

To solve the problem, we first need to identify all the individual forces acting on the connected bodies. Then, we can use vector addition to find the resultant force. Finally, we can use Newton's laws of motion to analyze the motion of the connected bodies and determine any other relevant quantities, such as acceleration or velocity.

5. Are there any real-world applications of solving the connected bodies problem with a resultant force of 39N?

Yes, there are many real-world applications, such as analyzing the forces acting on a bridge or a building, designing structures that can withstand certain forces, or predicting the motion of objects in a system. Understanding how forces act on connected bodies is also important in fields such as engineering, physics, and biomechanics.

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