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Old Oct 15th 2010, 08:22 PM   #1
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Elevator Problem

Alright so here's the problem.

"An elevator can move upwards at a maximum acceleration of 2 m/s/s. If
the cable pulling up the elevator car can stand a maximum tension in it
of 1,000 N, how many people (each of mass 50 kg) can safely ride in the
elevator when it is moving up at that maximum acceleration? Ignore the
mass of the elevator. Hint: Assume that the maximum number of people in
the elevator is X. Then, find the force due to gravity acting on these
people before finding the resultant force on them when the elevator
begins to ascend. After this apply Newton’s 2nd Law to solve for the
answer."

What I was thinking was Fnet is the weight times the acceleration. So if the acceleration is 2 m/s/s times the weight of one person which is 50 k that is 100 N force acting against the 1000. So would it be 10 people total max?
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Old Oct 15th 2010, 11:32 PM   #2
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A little problem here:

What I was thinking was Fnet is the weight times the acceleration.
It's not the weight times the acceleration but the mass times the acceleration.

Following this, the weight of 1 person will be 10 x 50 = 500 N.

Take your hint. Let X be the number of people.

The weight of X people will be 500X N.

Resultant force will be the tension minus the weight.

T - 500X = ma

Tension is 1000 N, mass is 50X and acceleration is 2.

1000 - 500X = 50X(2)

1000 - 500X = 100X

1000 = 600X

X = 1000/600 = 1.67

Well... only one person can take this elevator to use its maximum acceleration it seems
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