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# Force and motion: Forces on a kidney stone

## Problem

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 $3\phantom{\rule{0.167em}{0ex}}\text{mm}$ 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 $0.0015\phantom{\rule{0.167em}{0ex}}\text{kg}$. 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 ${\text{F}}_{1}$: The frictional force between the stone and the sides of the ureter
Force ${\text{F}}_{2}$: 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.
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?