Physics Review Notes - Ch. 2, Question 12

Hi Alex!

In Physics RN Chp 2 Quiz, theres a question (#12)

A 100 kg elevator accelerates up at rate a. What is the average force acting on the elevator if it covers a distance, x, over a period of 10 s?

So I knew I had to set up the opposing forces of both the elevator accelerating and mg. But I had set it up as F = ma-mg instead of what they had ma = F-mg. Is there a reason why it's one way or the other? (Or are they equivalent and I'm just not seeing how that is..)

Thanks!
-----------------------------
Thanks for the question.


Any time you have a kinematics question, you want to use a good three step method:
-Identify the forces with a FBD
-Write Newton's second law
-Solve for what they want


In this case, let's start with the forces.  We have gravity, as you mentioned.  We also have a force of tension causing the acceleration of the elevator.  Or we could simply call this the force applied (F_applied).  There are no other contact forces, gravitational forces, or electrostatic forces, so we're set.  We'll have F_applied pointing upwards, and gravity (mg) pointing downwards.


Now we write Newton's second law:
F_net = ma
The net force is F_applied - mg, derived from our free body diagram, so
F_net = F_applied - mg = ma
Solving for the applied force:
F_applied = ma + mg = m(a + g).


Hopefully this helps explain this part of the question.  I think the error you may have made was mixing up net force with applied force.  Note the subscripts in the math here!


Please let me know what other questions you have, or if you would like me to solve out the rest of the question for you.