A physical model of human sitting
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- A physical model of human sitting
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A physical model of human sitting
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[post_date] => 2025-01-09 07:40:32
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[post_content] => Practice Passage (Question 1-4)
*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 comfortable sitting position for a patient leaning back on a stool (Figure 1A) requires the weight and torque of the upper half of the body to exactly counterbalance the weight and torque of the lower half of the body. The hips of the patient serve as a pivot point for a simple balance, but they also allow the patient to adjust the angle of his posture,θ, so that he can maintain his balance
The patient can be modeled as two uniform rods with lengths H (the length from the top of the head to the hips) and L (the length from the hips to the feet) . By changing the angle θ between the torso and legs, the patient can adjust his balance.
Figure 1. The posture of a leaning man sitting balanced on a stool.
Suppose that the patient fails to maintain his balance and tilts off the stool and falls towards the ground. As he falls, his hips remain in contact with the stool without sliding, such that the motion of his head traces a circular arc around the point where his hips make contact with the stool. The patient can avoid hitting the ground only if he adjust the positions of his legs to counterbalance his torso.
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[question] => When the individual is sitting stationary in Figure 1, the net force acting on the individual points in which direction?
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[answer] => 2
[description] => Reason for the Correct Answer:
The sitting individual is motionless and thus is not accelerating
The upwards force exerted by the stool cancels the downwards force exerted by the weight of the individual
The net force on the individual is zero
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[answers] => Array
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[0] => Array
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[each_answer] => A. The direction depends on θ
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[1] => Array
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[each_answer] => B. The net force is zero
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[each_answer] => C. Upwards from the stool
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[3] => Array
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[each_answer] => D. Downwards towards the ground
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[1] => Array
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[quiz_unique_key] => 3873426850
[question] => Which of the following definitions accurately describes the sitting position in Figure 1?
[value] => Array
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[answer] => 3
[description] => Reason for the Correct Answer:
The man needs to actively use his muscles to regain his posture if the angle θ is disturbed
In stable equilibrium, the minimum of potential energy is at the equilibrium point
The patient, when set off balance, tends towards a position other than the equilibrium point
The patient sits in an unstable equilibrium
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[0] => Array
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[each_answer] => A. Non-equilibrium
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[each_answer] => B. Stable equilibrium
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[each_answer] => C. Unstable equilibrium
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[each_answer] => D. Anti-equilibrium
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[2] => Array
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[quiz_unique_key] => 83407773
[question] => The mass of the upper half of the body is 𝒎ₕ, and the distance of the center of mass from the hips is given by 
, whereas the mass of the lower half of the body is given by 𝒎ʟ, centered at a position 
below the hips. Which of the following relations accurately describes the equilibrated sitting position shown in Figure 1?
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[answer] => 1
[description] => Reason for the Correct Answer:
In order to remain balanced, the torque acting on one half of the body must counterbalance the torque acting on the other half of the body
The torque is proportional to the force of gravity, multiplied by the perpendicular distance from the pivot to the point at which it acts.
The perpendicular distance from the pivot to the point at which gravity acts on the torso center of mass is given by 
The torque is balanced when 
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[each_answer] => A. 
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[each_answer] => B. 
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[each_answer] => C. 
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[each_answer] => D. 
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[quiz_unique_key] => 2261298308
[question] => In which approximate direction is the net force on the patients torso oriented as he falls, as described in the last paragraph?
[value] => Array
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[answer] => 3
[description] => Reason for the Correct Answer:
Because the man traces a circular trajectory, the stool exerts a frictional force perpendicular to gravity that prevents him from sliding.
This frictional force needs to be added to the contributions of gravity in determining the net resultant force.
Because the force due to gravity has a constant direction, and the centripetal force points towards the stool, the sum of the forces changes direction as the man falls
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[answers] => Array
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[each_answer] => A. Downwards towards the ground
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[each_answer] => B. Upwards from the stool
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[each_answer] => C. The direction varies as the man falls
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[each_answer] => D. Along the direction of the torso, towards the hips
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