Forces acting on a box-pulley system in an elevator?

[Sagrebella]

Was the mass of block A 3.4 kg or 3.8 kg? I seem to recall it being 3.8 kg.

Oh my goodness, you're absolutely right. I used the wrong value for mass. Thank you so much for catching that error. With that changed, my answer is now 20.1 N, which is the correct answer on my homework website!

Thank you so much for your help with this problem gneill. Again, your explanations helped clarify a lot. I will probably be back with more questions in the future. I hope I will receive your guidance again during those difficult times and I promise to have a free body diagram and my attempts written out beforehand when I come back.

 

[gneill]

Glad to be of help! See you next time.

 

[cjm]

Ok, that makes sense.

and thank you again for your clear explanation, I re-did my equation, taking into mind that the box is stationary on the floor. Also, I changed my overly-rounded answer to 11.8 N instead of 12 N. Hopefully that works.

Now,

F_N + F_T - F_G = 0

F_N + 11.8 - m(g-a) = 0

F_N + 11.8 - 3.4(10-1.6) = 0

F_N + 11.8 - 28.56 = 0

F_N = 16.8 N

Why do we use "m(g-a)" instead of mg? IS it because we have to take the difference of the accelerations because theyre both going in the same direction?

 

[kuruman]

Why do we use "m(g-a)" instead of mg? IS it because we have to take the difference of the accelerations because theyre both going in the same direction?

Yes. Also, if the elevator were accelerating up, you would use "m(g+a)". If the elevator were not accelerating, you would use just "mg".