- calculusxy

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.

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- calculusxy

- 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|

- 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

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## More answers

- 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

- 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.

- 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

- calculusxy

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

- calculusxy

*formula

- 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

- calculusxy

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

- 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

- calculusxy

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

- 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?

- calculusxy

yes

- Michele_Laino

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

- calculusxy

ok

- Michele_Laino

that fictitious force will add to your weight force

- calculusxy

ok

- calculusxy

can we use the formula f = m x a?

- Michele_Laino

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

- Michele_Laino

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

- calculusxy

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

- Michele_Laino

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

- Michele_Laino

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

- calculusxy

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

- Michele_Laino

ok!

- Michele_Laino

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

- calculusxy

that's the potential energy right?

- Michele_Laino

yes!

- calculusxy

27440

- Michele_Laino

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

- Michele_Laino

correct!

- calculusxy

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

- Michele_Laino

hint:
70*2*40=5600

- calculusxy

i got lost after finding the force.

- Michele_Laino

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

- calculusxy

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

- Michele_Laino

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

- Michele_Laino

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

- calculusxy

give me a minute...

- calculusxy

so i do 27440 +5600= 33040

- Michele_Laino

that's right!

- calculusxy

so that's my answer right?

- Michele_Laino

yes!

- calculusxy

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

- Michele_Laino

ok!

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