# Elevator question

100 kg elevator acclerates up at rate avg a*. What's the avg force acting on the elevator if it covers a distance X over a period of 10s?

a* denotes average accleration
a. 2X + 1000
b. 100(a* + 1)
c. 2a* + 1000
d. 2a*X

I set up a free body diagram to show all the forces acting on the elevator. There's a downward force due to gravity, Fg, the net upward force, Fn, causing the accleration.

Fn - Fg = ma*
Fn = ma* + Fg

The question states that it travels a distance of X over 10 sec

a* = delta V/delta t
delta V = X/t , which the question gives me
delta V = x/10s, i substituted this into the a* equation and got
a* = x/100s

when i plug this into my net force equation:

Fn = ma* + Fg
Fn = m(a* + g)
Fn = 100kg(x/100s + 10m/s^2)
Fn = X + 1000

I can't seem to figure out why my answer doesn't match any of the answer choices. Can someone please point out what i'm doing wrong?
Thanks

You used the wrong kinetic equation. You calculated your final velocity incorrectly.

You used the wrong kinetic equation. You calculated your final velocity incorrectly.

avg velocity comes to mind since the question says the elevator travels a distance x over a period of 10s. If i solve the problem using this information, the answer comes out to be 2X + 1000.
But avg accleration is equal to delta v/ delta t, not avg velocity. And also, using avg velocity would mean i have constant acceleration and i don't.

I really think this is a ridiculous question, very loosely termed.

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Doc Al
Mentor
a* = delta V/delta t
OK.
delta V = X/t , which the question gives me
No, X/t gives the average speed, not the change in speed.

ok, so does that mean avg speed is = 2X/t?
if so, then the answer is a. 2X + 1000

I still don't see the relationship between avg speed and avg acceleration.

HallsofIvy
Homework Helper
ok, so does that mean avg speed is = 2X/t?
if so, then the answer is a. 2X + 1000

I still don't see the relationship between avg speed and avg acceleration.
There isn't any. And average speed is irrelevant. Force= mass * acceleration, not mass* speed. If the speed were constant over the trip, there would be no force.

There isn't any. And average speed is irrelevant. Force= mass * acceleration, not mass* speed. If the speed were constant over the trip, there would be no force.

ok, if the acceleration were constant and the initial velocity were given to be 0, then i see some sense in solving this problem. And even then the answer wouldn't match any of the given answers.

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