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A curve of radius 151 m is banked at an angle of 11°. An 838-kg car negotiates the curve at 86 km/h without skidding. Neglect the effects of
Question
A curve of radius 151 m is banked at an angle of 11°. An 838-kg car negotiates the curve at 86 km/h without skidding. Neglect the effects of air drag and rolling friction. Find the following.
(a) the normal force exerted by the pavement on the tires
kN ?
(b) the frictional force exerted by the pavement on the tires
kN ?
(c) the minimum coefficient of static friction between the pavement and the tires?
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Physics
3 years
2021-08-23T04:50:25+00:00
2021-08-23T04:50:25+00:00 1 Answers
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Answers ( )
a) 8.52 kN
b) 0.74 kN
c) 0.087
Explanation:
a)
There are 3 forces acting on the car on the banked curve:
– The weight of the car, , vertically downward
– The normal force of the pavement on the tires, N, upward perpendicular to the road
– The force of friction, , down along the road
Resolving the 3 forces along two perpendicular directions (horizontal and vertical), we obtain the equations of motions:
x- direction:
(1)
y- direction:
(2)
where
is the angle of the ramp
is the force of friction
m = 838 kg is the mass of the car
r = 151 m is the radius of the curve
is the speed of the car
Solving eq.(2) for Ff and substituting into eq.(1), we can find the normal force:
From (2):
(3)
Substituting into (1) and re-arranging,
b)
The frictional force between the pavement and the tires, , can be found by using eq.(3) derived in part a):
where we have:
is the normal force
is the angle of the ramp
m = 838 kg is the mass of the car
is the acceleration due to gravity
Substituting the values, we find:
c)
The force of friction between the road and the tires can be rewritten as
where
is the coefficient of static friction
N is the normal force exerted by the road on the car
In this problem, we know that
N = 8.52 kN is the normal force
is the frictional force
Therefore, the minimum coefficient of static friction between the pavement and the tires is: