A standard parking space is about 2.5 m wide and this parking lot is sloped at t

Question

A standard parking space is about 2.5 m wide and this parking lot is sloped at the 2. maximum allowable angle of 5 degrees. Find the maximum value for the coefficient of friction that will allow you roll the width of the parking lot without stopping. Write out your process in a clear, easy-to-follow manner. Here's some helpful information: a. This parking lot is 20 parking spaces wide b. You have the mass of an average human at 60 kg c. The shopping cart's mass is 20 kg d, v° = 7 m/s e. Use g = 10 m/s

Explanation / Answer

2. given, parking space width, w = 2.5 m

angle of slope, theta = 5 deg

coeff of friciton = mu

total number of spaces, n = 20

total wodth, d = n*w = 20*2.5 = 50 m

initial speed, vo = 7 m/s

total mass, m = 60 + 20 = 80 kg

hence normal reaction force on wheels of shopping cart, assuming four wheels = N

from force balance

4N = mg*cos(theta)

assume friction force f

when

from force balance

mgsin(theta) + 4f = ma ( where a is acceleration of the system)

also

N = mu*f

hence for roling distance d, maximum value of coefficient friction has to be found

this happens when the cart comes to a final speed vf = 0 m/s at the end of the parking lot

hence

2*a*d = vf^2 - vo^2

2*a*50 = -49

a = -0.49 m/s/s

hence

80*9.81*sin(5) + mu*80*9.81*cos(5) = 80*0.49

hence

mu = 0.03734

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