Running, Static Friction, Torques
Location: Outside U.S.
Date: April 28, 2011
My question is about the forces and torques required to
run fast and come to a stop. My thinking is this: When you run fast
(to the right say) and set your feet in order to stop, you have your
weight back at the moment you set your feet. There are three forces
acting on you: gravitation, friction, and normal force from the
floor (excluding air). Only the frictional force reduces my
horizontal speed. I can sum torques about any point so I choose to
sum torque about the center of mass. Gravity produces no torque.
Normal force produces torque that rotates my body counter-clockwise
and torque from friction rotates me clockwise. The net torque is due
to friction, which is why I rotate clockwise. Once I have my center
of mass above my feet, I have stopped rotating. So at some point,
the Normal force starts producing more torque than friction. But the
horizontal distance between my center of mass and my feet is getting
shorter as the torque from this force gets stronger relative to the
torque from friction. Either the Normal force must get stronger or
friction must get weaker as I slow down, or both
Because you choose to use center of mass as the pivot point around which
torque is calculated, gravity never produces torque for you. You are
correct about friction getting weaker. This is static friction, not
kinetic (or sliding) friction. Your shoes do not slide on the ground.
As the force needed to keep your feet from sliding on the ground
decreases, the friction decreases. Static friction is only as big as it
has to be.
Dr. Ken Mellendorf
Illinois Central College
Friction gets weaker. Static friction basically is a force of constraint, it is whatever is necessary to keep contacting surfaces from slipping. The formula with the coefficient of friction gives a maximum value, but the actual friction force can be anything less than that in magnitude. You can feel that as you stop: there is zero sideways force (friction) when you are standing still, unless you have your feet planted very far apart.
Richard E. Barrans Jr., Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming
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