An elevator in a hospital
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- An elevator in a hospital
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An elevator in a hospital
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[post_date] => 2025-01-09 07:26:53
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[post_content] => Practice Passage (Question 1-5)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
A hospital that specializes in orthopedic surgery and rehabilitation is investigating the accelerations experienced by patients while riding the hospital elevators so as to make sure they don’t cause pain to healing knees, ankles, and hips. To measure the acceleration of the elevators, the hospital placed a copper mass on an electronic scale that sat on the floor of the elevator.
The graph shown below is for a trial where the copper mass rides in the elevator from the bottom floor to the top floor. The elevator starts from rest, gets up to speed, travels upwards with constant speed, then slows down and stops at the top floor.
A similar trial was then conducted with a patient volunteer with knee arthritis. The patient stood on a scale in the elevator as it replicated the accelerative procedure. He then provided feedback on which portion of the journey was most physically taxing.
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[question] => During the portion of the trip where the elevator is moving upwards with constant velocity, how will the scale reading compare to the weight of the copper?
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[description] => Reason for the Correct Answer:
Constant velocity means the acceleration is zero.
Think about ΣF=0.
Since ΣF=0, F(scale) – mg = 0, or F(scale) = mg
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[each_answer] => A. It is impossible to tell without knowing the weight of the copper.
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[each_answer] => B. The scale reading will be equal to the weight of the copper.
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[each_answer] => C. The scale reading will be larger than the weight of the copper.
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[each_answer] => D. The scale reading will be smaller than the weight of the copper.
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[1] => Array
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[quiz_unique_key] => 3873426850
[question] => What is the mass of the copper? (Assume g=10m/s²)
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[answer] => 2
[description] => Reason for the Correct Answer:
The copper mass only accelerates during two portions of the trip.
Since the copper mass is not accelerating between t=0 and t=2 seconds, you can use ΣF=0
The scale reading gives the normal force on the copper mass.
ΣF = 0, F(scale) – mg = 0, 300N-mg = 0, m = 30kg
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[answers] => Array
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[each_answer] => A. 10 kg
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[each_answer] => B. 30 kg
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[each_answer] => C. 25 kg
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[each_answer] => D. 40 kg
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[question] => What is the magnitude of the acceleration of the elevator between times t = 2sec and t = 3sec?
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[answer] => 3
[description] => Reason for the Correct Answer:
Use ΣF = ma
Since the copper mass is not initially accelerating between t=0 and t=2 seconds, you can use ΣF=0 to calculate the mass of the copper object. Since ΣF=0, Fscale – mg = 0, 300N – mg = 0, m = 30.6kg.
F(scale) – mg = ma
400N – 30kg (9.8m/s²) = (30kg)a, which means a = 3.3m/s²
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[answers] => Array
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[each_answer] => A. 4.5 m/s²
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[each_answer] => B. 2.9 m/s²
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[each_answer] => C. 3.3 m/s²
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[each_answer] => D. 1.7 m/s²
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[question] => What is the magnitude of the acceleration of the elevator between times t = 8 sec and t = 9 sec?
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[answer] => 3
[description] => Reason for the Correct Answer:
Use ΣF = ma. Also use the mass of the copper calculated in the previous questions.
F(scale) – mg = ma
250N – 30kg (10m/s²) = (30kg)a, which means a = -1.7m/s². Remember that the magnitude refers to just the absolute value of this number, so the answer is 1.7 m/s².
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[each_answer] => A. -1.7m/s²
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[each_answer] => B. 0.8m/s²
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[each_answer] => C. 1.7m/s²
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[each_answer] => D. 2.5m/s²
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[question] => During which portion of the trip would the volunteer patient most likely report greatest discomfort?
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[answer] => 4
[description] => Reason for the Correct Answer:
Due to the patient’s arthritis, the patient will feel the most discomfort when their knees experience the greatest force.
The patient’s knees will feel the greatest force when the normal force is greatest.
The normal force will be greatest when the acceleration is greatest in the upwards direction.
The acceleration is greatest between 2-3sec.
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[each_answer] => A. 0-2 sec
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[each_answer] => B. 8-10 sec
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[each_answer] => C. 3-8 sec
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[each_answer] => D. 2-3 sec
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The graph shown below is for a trial where the copper mass rides in the elevator from the bottom floor to the top floor. The elevator starts from rest, gets up to speed, travels upwards with constant speed, then slows down and stops at the top floor.
A similar trial was then conducted with a patient volunteer with knee arthritis. The patient stood on a scale in the elevator as it replicated the accelerative procedure. He then provided feedback on which portion of the journey was most physically taxing.
[post_title] => An elevator in a hospital
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[post_status] => publish
[comment_status] => closed
[ping_status] => closed
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