Estimation problem: A) What’s the minimum coefficient of friction between Tori B

Question

Estimation problem: A) What’s the minimum coefficient of friction between Tori Bowie’s track shoes and the track? (Hint: figure this based on her acceleration in the 100 meter sprint.)
Estimation problem: A) What’s the minimum coefficient of friction between Tori Bowie’s track shoes and the track? (Hint: figure this based on her acceleration in the 100 meter sprint.)
Estimation problem: A) What’s the minimum coefficient of friction between Tori Bowie’s track shoes and the track? (Hint: figure this based on her acceleration in the 100 meter sprint.)

Explanation / Answer

her 100 m timing is 10.91 second.

assuming constant acceleration for 50 m and constant deceleration for 50 m

let acceleration and deceleration magnitude be a .

for first 50 meters, if time taken is t1 seconds:

maximum speed at the end of t1 seconds=v=a*t1

if time for second 50 meters is t2,

then v/t2=a

using v=a*t1,a*t1/t2=a==>t1=t2

as t1+t2=10.91,t1=t2=10.91/2=5.455 seconds

as area under velocity -time graph is total distance covered

0.5*time period* maximum speed=100

==>0.5*(t1+t2)*a*t1=100

given t1+t2=10.91

==>0.5*10.91*a*5.455=100

==>a=3.3606 m/s^2

so coefficient of friction=a/g

=0.34291

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