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

[ayans2495]

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

 

[ayans2495]

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]

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.

 

[berkeman]

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.

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.

 

[haruspex]

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
...