Standing balance
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Standing balance
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[post_date] => 2025-01-09 07:38:22
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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 simple model of human standing is given by an inverted pendulum, a one-dimensional, classical model for the motion of a single, massive particle (Figure 1). A standing human is approximated as a single mass (located at the center of mass) separated from the ground by a massless rod of fixed length L. The feet are treated as attached to the ground by a fulcrum, such that the center of mass can only undergo motion along an arc of radius L around the feet---thus the mechanics of the system are described by the tilt angle θ, representing the angular displacement of the center of mass from directly above the feet, with the rod positioned normal to the ground. The pendulum is perfectly balanced when the mass is positioned directly above the pivot point; however, a very slight displacement of the mass from this position will cause the pendulum to tip over.
Figure 1. The analogy between a standing patient and an inverted pendulum.
Humans can overcome this difficulty and maintain standing balance, at which the system is at equilibrium, by maintaining active control of the position of their center of mass relative to the fulcrum formed by their feet. For small displacements, the ankles work to exert a torque that counteracts gravity and prevents the individual from falling over. The timescale that this restoring force must act to recover equilibrium is proportional to the period of a simple pendulum, demonstrated by Equation 1.
Precise measurements of active balancing can be made by filming an individual and digitally tracking the location of the center of mass after the t = θ. A sample figure showing the angular response is given in Figure 2. Surprisingly, these measurements show that the seemingly inert process of standing consists of many coordinated ankle motions that stabilize the body after it undergoes slight deflections.
Figure 2. Simulated data showing the time-varying tilt angle of a standing individual who was tilted forward by 0.2 radians at t = θ, and who is actively returning to their original vertical standing position.
Concept adapted from: Winter, D. A. (1995). Human balance and posture control during standing and walking. Gait & Posture, 3(4), 193-214.
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[question] => Which of the following correctly describe the difference between an inverted pendulum (as shown in in Figure 1) and a standard pendulum with identical length and mass?
I. An inverted pendulum has minimal kinetic energy when it reaches its equilibrium point
II. An inverted pendulum requires a non-gravitational restoring force to remain in equilibrium
III. An inverted pendulum reaches a higher maximum gravitational torque
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[answer] => 3
[description] => Reason for the Correct Answer:
The maximum torque due to gravity is Lmg in both cases–for the inverted pendulum, this maximum is reached just before the mass collides with the ground.
The kinetic energy is minimal when an individual is standing (equilibrium)
Standing requires the influence of the ankles (an external force) to maintain the otherwise unstable equilibrium.
Only I and II are accurate statements.
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[each_answer] => A. I and III
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[each_answer] => B. II and III
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[each_answer] => C. I and II
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[each_answer] => D. I, II, and III
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[quiz_unique_key] => 3873426850
[question] => Suppose a standing person loses their balance by tripping forward by a fixed angle (theta). Which of the following quantities would be greater for a taller person than a short person of equal mass?
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[answer] => 2
[description] => Reason for the Correct Answer:
The relevant timescale for the ankles to restore balance is given by the period of a simple pendulum, the rate is the inverse of this timescale.
The period of a simple pendulum increases with increasing length
The total gravitational force is the same for two objects of equal mass
The torque, for a fixed angular displacement, is given by mgL sin(θ)
The taller person’s ankles must counteract a greater gravitational torque
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[0] => Array
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[each_answer] => A. The initial angular speed immediately after tripping forward
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[1] => Array
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[each_answer] => B. The torque that must be exerted by the ankles in order to restore balance.
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[each_answer] => C. The total gravitational force acting on the center of mass
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[each_answer] => D. The rate at which the ankles must exert a given torque in order to regain balance
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[quiz_unique_key] => 83407773
[question] => In Figure 2, which of the following sets the initial amplitude at t = θ?
[value] => Array
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[answer] => 1
[description] => Reason for the Correct Answer:
The graph depicts only information about the response of the standing individual after a sudden tilt at t = 0
The acceleration due to gravity sets the frequency of a simple pendulum, and so it determines the response time to equilibrate an inverted pendulum.
The rate of a force application does not uniquely determine the amount by which the individual tilts forward
The initial amplitude represents the initial tilt of the individual.
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[0] => Array
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[each_answer] => A. The angular distance by which the person initially tilts forward
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[each_answer] => B. The rate of the sudden tilt just before t = θ.
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[each_answer] => C. magnitude of gravitational acceleration
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[each_answer] => D. The mass of the individual
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[question] => In Figure 2, which of the following determines the frequency of the decaying oscillations?
[value] => Array
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[answer] => 3
[description] => Reason for the Correct Answer:
The rate of the initial tilt does not affect the response of the system after the cessation of the tilting force
The magnitude of the initial tilt does not affect the response of the system after the cessation of the tilting force.
The period of a simple pendulum is independent of the mass.
The acceleration due to gravity sets the frequency of a simple pendulum, and so it determines the response time to equilibrate an inverted pendulum.
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[each_answer] => A. The angular distance by which the person initially tilts forward
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[each_answer] => B. The rate of the sudden tilt just before t = θ.
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[each_answer] => C. The magnitude of gravitational acceleration
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[each_answer] => D. The mass of the individual
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[question] => Which of the following provides the most likely explanation for the decrease in amplitude of successive peaks of the sinusoidal response in Figure 2?
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[answer] => 1
[description] => Reason for the Correct Answer:
With a fatiguing restoring force, the amplitude would increase in successive cycles as the ankles increasingly fail to counteract gravity
The potential energy is greatest when the angular displacement is zero, towards which the signal decays.
The torque increases with the tilt angle, and the angle of the torque does not contribute to the amplitude of the signal in successive cycles.
The decay in amplitude of oscillations is most likely the result of frictional or feedback damping dissipating the energy stored in the oscillations.
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[answers] => Array
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[0] => Array
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[each_answer] => A. Energy exiting the system due to damping effects.
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[each_answer] => B. Gravitational potential energy being dissipated as heat.
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[each_answer] => C. Fatigue in the ankles providing the restoring force.
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[each_answer] => D. As the tilt angle changes, the torque decreases.
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Figure 1. The analogy between a standing patient and an inverted pendulum.
Humans can overcome this difficulty and maintain standing balance, at which the system is at equilibrium, by maintaining active control of the position of their center of mass relative to the fulcrum formed by their feet. For small displacements, the ankles work to exert a torque that counteracts gravity and prevents the individual from falling over. The timescale that this restoring force must act to recover equilibrium is proportional to the period of a simple pendulum, demonstrated by Equation 1.
Figure 2.