## calculusxy one year ago MEDAL!!! How much work is done by an elevator that carries a person with a mass of 70 kg up 40 meters? Assume the elevator has a constant acceleration of 2 m/s^2.

1. calculusxy

@Michele_Laino

2. Michele_Laino

The elevator is not a inertial system, nevertheless, we can consider it, as an inertial system if we introduce the fictitious force -m*Ac where Ac is the ecceleration of the elevator, and m is the mass of the person inside the elevator. So the situation is like below: |dw:1437833008631:dw|

3. Michele_Laino

in other word, on the person are acting two forces: the weight force whose magnitude is m*g= 70*9.81=...newtons the fictitious force, whose magnitude is m*Ac=70*2=...newtons Since the elevator is a inertial system, the laws of physics apply unchanged in it, so the requested work is: $\Large W = m\left( {g + {A_c}} \right)h = ...joules$ where h=40 meters

4. calculusxy

So we are learning about energy now and the formulas that we have gone through so far are: Power = w/t Work = f x d Potential Energy: mass x gravity x distance Kinetic Energy: 1/2mv^2

5. calculusxy

The teacher said that he incorporated these formulas into the questions, so i need to understand what formulas go to what question to get the answer.

6. Michele_Laino

you can apply this formula: Work = f x d providing that the force f is: f= m(Ac+g) where Ac=2 m/sec^2

7. calculusxy

Why can't we use the formulas to find the power because that this the amount of work done in an interval?

8. calculusxy

*formula

9. Michele_Laino

the elevator is not an inertial system, since there are 2 forces acting on the person inside the elevator. I think it is better if we use the formula: work = force * distance

10. calculusxy

I still don't understand how you find the force.

11. Michele_Laino

In other words, I have applied the Principle of Equivalence, and I consider the elevator like an inertial system, providing that to introduce the fictitious force

12. calculusxy

i am sorry , but i don't know the principle of equivalence because i am just a rising eighth grader.

13. Michele_Laino

when you use an elevator in order to go up, at the starting of motion, you feel like pressed towards the floor of the elevator, right?

14. calculusxy

yes

15. Michele_Laino

that is due to the fictitious force which is acting on you

16. calculusxy

ok

17. Michele_Laino

18. calculusxy

ok

19. calculusxy

can we use the formula f = m x a?

20. Michele_Laino

so the total force which is acting on you is: fictitious force+weight force

21. Michele_Laino

and the work done by the elevator is the work done by that total force

22. calculusxy

$Force = mass \times acceleration$ $Force = 70 kg \times 2m/s^2$ $Force = 140 N$ Work: $Force \times Distance$ $140N \times 40 m$ $1600J$

23. Michele_Laino

yes! the fictitious force is given by the subsequent formula: f=m*Ac where Ac=2 m/sec^2

24. Michele_Laino

now you have to add the work done by the weight force

25. calculusxy

Oh... i am sorry about misinterpreting it because i didn't know that Ac actually meant acceleration.

26. Michele_Laino

ok!

27. Michele_Laino

the work done by the weight force is: 70*9.8*40=...?

28. calculusxy

that's the potential energy right?

29. Michele_Laino

yes!

30. calculusxy

27440

31. Michele_Laino

the work done against the weight force is equal to the potential energy gained by the elevator

32. Michele_Laino

correct!

33. calculusxy

And now I have to add it: 27440 + 1600 = 29040

34. Michele_Laino

hint: 70*2*40=5600

35. calculusxy

i got lost after finding the force.

36. Michele_Laino

so, we have: 27440+5600=...

37. calculusxy

but why did we need to do 70*2*40?

38. Michele_Laino

the work done by the fictitious force, is : m*Ac*h= 70*2*40=...

39. Michele_Laino

${\text{work = force }} \times {\text{ distance = }}\left( {{\text{m}} \times {{\text{A}}_{\text{c}}}} \right) \times {\text{h}}$

40. calculusxy

give me a minute...

41. calculusxy

so i do 27440 +5600= 33040

42. Michele_Laino

that's right!

43. calculusxy

44. Michele_Laino

yes!

45. calculusxy

thank you!!! i have another question may i ask that as well?

46. Michele_Laino

ok!