A 1200 kg car rounds a curve on a flat road of radius 52 m at a speed of 36 km/hr will the car turn if the pavement is dry and coefficient of static friction is 0.45
Answers
Explanation:
To find a force we need to know something about a mass, and we haven't been told the mass of the car. Let's just call it '
m
' and leave it at that for the moment, because I have a feeling it will cancel out in the end.
The centripetal force is given by
F
cent
=
m
a
=
m
v
2
r
We have values for the velocity and the radius, so:
F
cent
=
m
×
14
2
50
=
3.92
m
N
The frictional force must be equal to or greater than this force in order for the car to successfully make it around the curve without sliding out.
The frictional force will be given by:
F
frict
=
μ
F
norm
Where
F
norm
is the normal force, equal to
m
g
.
We can equate these two forces, the frictional force and the centripetal force:
F
cent
=
F
frict
3.92
m
=
μ
m
g
We can cancel out a factor of
m
in both sides and rearrange to make
μ
the subject:
μ
=
3.92
g
Substituting in the value
g
=
9.8
m
s
−
2
,
μ
=
3.92
9.8
=
0.4