If an eighteen wheeler has a mass of 36287 kg and is traveling at a speed of 70mph , how long would a sand ramp have to be to stop the truck given its breaks don’t work? The coefficient of friction of sand is 0.60.

F= ma

F

_{fr}= µF_{N}= µmg
F

_{N}= mg
µmg = ma

(0.60)(36287kg)(9.8) = (36287kg)a

a = 5.88 m/s

^{2}
Δt

70mph = 31.3 m/s

5.88 m/s

^{2}=__31.3 – 0__
Δt

Δt = 5.32 s

x = v

_{0}t + ½ at^{2}
x = (31.3m/s)(5.32s) + ½ (5.88m/s

^{2})(5.32s)^{2}
x = 250 m

The ramp must be at least 250 m long to
stop a truck traveling at 70mph.

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