Two Man Sled Ride with Friction

Classical Mechanics Level pending

A two person sled slides down a 750 ft. long hill. The hill gradient is 5/12 (vertical/horizontal). The combined weight of the people and sled is 600 lbs. If the coefficient of kinetic friction is 1/50 and the wind resistance is 5 times the velocity, at what time in seconds will they reach the bottom of the hill? Provide answer to nearest 10th. g=32.2 ft/s^2


The answer is 20.8.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Steven Chase
Mar 23, 2020 
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import math

L = 750.0
theta = math.atan(5.0/12.0)
W = 600.0
uk = 1.0/50.0
g = 32.2
m = W/g

###################################

t = 0.0
dt = 10.0**(-5.0)

x = 0.0
xd = 0.0
xdd = 0.0

while x <= L:

    x = x + xd*dt
    xd = xd + xdd*dt

    F = W*math.sin(theta) - uk*W*math.cos(theta) - 5.0*xd

    xdd = F/m

    t = t + dt

###################################

print dt
print t

#>>> 
#0.0001
#20.7821
#>>> ================================ RESTART ================================
#>>> 
#1e-05
#20.7819399994
#>>>

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