A cyclist is riding his bike up a mountain trail. When he starts up the trail, he is going 8 m/s. As the trail gets steeper, he
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Answer:
0.767
Explanation:
The work done on the truck by the frictional drag force is given by
where
F is the magnitude of the frictional force
d = 38.0 m is the maximum displacement allowed for the truck
The negative sign is due to the fact that the force of friction is opposite to the motion of the truck
The force of friction can also be written as:
where
is the coefficient of kinetic friction between the truck and the lane
m is the mass of the truck
g is the acceleration of gravity
So we can rewrite the work done as
(1)
According to the work-energy theorem, the work done by friction is equal to the change in kinetic energy of the truck:
(2)
where
v = 0 is the final velocity of the truck
u = 23.9 m/s is the initial velocity of the truck
By combining (1) and (2) we get
And solving for , we find the minimum coefficient of kinetic friction able to stop the truck in a distance d: