Forces on a kidney stone
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- Forces on a kidney stone
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Forces on a kidney stone
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[post_date] => 2025-01-09 07:25:59
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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 renal calculus, otherwise known as a kidney stone, is a solid formation of urinary minerals found in the urinary system. Kidney stones often pass through the urinary tract undetected, although they begin to obstruct the pathway when they grow to 3mm in size or greater. This process involves both walls of the ureter applying force on the kidney stone until it no longer moves. In these instances, they may cause pain and, in extreme cases, can require surgery.
A patient has a kidney stone of mass 0.0015 kg. The kidney stone is moving at a constant velocity from the kidney to the bladder via a path through the ureter tube as seen below.
Figure 1. A kidney stone passing from the kidney, through the ureter, towards the bladder.
Assume that the only significant forces acting on the kidney stone in this case are as follows:
Force F1: The frictional force between the stone and the sides of the ureter
Force F2: The force pushing the kidney stone towards the bladder, caused by pressure behind the kidney stone
Note: Assume that the force of gravity on the kidney stone can be ignored since it is so small compared to the size of Force 1 and Force 2.
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[question] => During a certain time interval, the kidney stone is moving toward the bladder with constant velocity. How must the magnitude of Force 2 compare with the magnitude of Force 1 during this time?
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[answer] => 4
[description] => Reason for the Correct Answer:
Use Newton’s first law.
Newton’s first law says that objects will continue in a state of constant velocity unless there is an external unbalanced force on the object.
This stone is moving with constant velocity, so the forces on it must be canceling. The forces can only cancel each other if they are equal in magnitude.
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[each_answer] => A. The magnitude of Force 2 is larger than the magnitude of Force 1.
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[each_answer] => B. Either force could have larger magnitude depending on how fast the kidney stone is moving.
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[each_answer] => C. The magnitude of Force 1 is larger than the magnitude of Force 2.
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[each_answer] => D. The magnitude of Force 1 is equal to the magnitude of Force 2.
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[question] => At another time, the forces on the kidney stone are as follows: F2=0.045N and F1=0.015N. While these forces act, what would be the acceleration of the kidney stone?
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[answer] => 3
[description] => Reason for the Correct Answer:
Because F₂ > F₁, the direction of the net force is towards the bladder. ΣF= F₂ – F₁= 0.045 – 0.015 = 0.030 N
Newton’s second law says ΣF=ma.
Plug in ΣF= 0.030 N and m=0.0015 kg into ΣF=ma to get 0.030 N = (0.0015kg)a. Solve for a: a = 0.030 / 0.0015 = 20.0 m/s²
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[each_answer] => A. 10 m/s² toward the bladder
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[each_answer] => B. 20 m/s² toward the kidney
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[each_answer] => C. 20 m/s² toward the bladder
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[each_answer] => D. 10 m/s² toward the kidney
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[question] => During another time, the forces on the kidney stone are as follows: F2 = 0.035N and F1 = 0.085N. With these forces, is it possible for the kidney stone to be moving towards the bladder?
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[answer] => 2
[description] => Reason for the Correct Answer:
Think of Newton’s Second Law ΣF=ma.
Velocity does not have to point in the same direction as the acceleration.
Since the force towards the kidney is larger than the force towards the bladder, the acceleration will point towards the kidney.
The kidney stone can be moving towards the bladder with acceleration towards the kidney if the stone is slowing down.
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[each_answer] => A. Yes, any time there is a force towards the bladder, the kidney stone will move that way.
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[each_answer] => B. Yes, but the kidney stone would have to be slowing down.
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[each_answer] => C. Yes, but the kidney stone would have to be speeding up.
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[each_answer] => D. No, since the force towards the kidney is larger the kidney stone must be moving towards the kidney.
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[question] => Assume that the force F₂ on the kidney stone is due to fluid built up in the ureter behind the kidney stone. If the force F₁ = 0.06N on the kidney stone, what is the force exerted on the kidney from the fluid build up?
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[answer] => 2
[description] => Reason for the Correct Answer:
Use Newton’s third law
Newton’s third law says that every force has an equal and opposite force.
Since the force from the fluid on the kidney stone is 0.06 N, then the force of the kidney stone on the fluid is 0.06 N. This will cause a fluid force on the kidneys of 0.06 N.
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[each_answer] => A. 0.03 N
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[each_answer] => B. 0.06 N
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[each_answer] => C. 0 N
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[each_answer] => D. 0.12 N
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[question] => Which of the following changes would make the kidney stone harder to pass?
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[answer] => 1
[description] => Reason for the Correct Answer:
The pressure between stone and kidney helps pass the stone; the pressure between the bladder and stone prevents passing of the stone.
Friction is opposing the passing of the stone.
A greater normal force would increase the kinetic friction between the stone and the ureter, which would make it harder to pass.
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[each_answer] => A. Greater normal force between ureter wall and kidney stone
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[each_answer] => B. Greater fluid pressure between stone and kidney
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[each_answer] => C. Greater thickness of ureter walls
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[each_answer] => D. Smaller fluid pressure between stone and bladder
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