Solve Elevator Force: 100kg, X, 10s, a*

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In summary, the elevator accelerates at an average rate of a*. The average force acting on the elevator is 100kg.
  • #1
HumorMe81
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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
 
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  • #2
You used the wrong kinetic equation. You calculated your final velocity incorrectly.
 
  • #3
flatmaster said:
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.
 
Last edited:
  • #4
HumorMe81 said:
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.
 
  • #5
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.
 
  • #6
HumorMe81 said:
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.
 
  • #7
HallsofIvy said:
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.
 
Last edited:

What is the formula for calculating elevator force?

The formula for calculating elevator force is F = ma, where F is the force, m is the mass, and a is the acceleration.

How do you solve for X in the equation?

To solve for X, you would need to rearrange the equation to isolate X. In this case, X = F/(ma). Plug in the given values for mass (100kg), acceleration (a), and force (F) to solve for X.

What is the unit of measurement for elevator force?

The unit of measurement for elevator force is typically expressed in newtons (N).

What is the significance of the given time (10 seconds) in the equation?

The given time (10 seconds) is the amount of time it takes for the elevator to reach its final velocity. This value is needed in order to calculate the acceleration (a) of the elevator.

How does the mass of the elevator affect the elevator force?

The mass of the elevator directly affects the elevator force, as it is a component in the formula for calculating force. The greater the mass, the greater the force needed to accelerate the elevator to the given velocity.

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