Answer:
What is the magnitude of the centripetal acceleration of a car following a curve of radius 500 m at a speed of 25.0 m/s (about 90 km/h)? Compare the acceleration with that due to gravity for this fairly gentle curve taken at highway speed. See Figure 2a.
Strategy
Because v and r are given, the first expression in
a
c
=
v
2
r
;
a
c
=
r
ω
2
a
c
=
v
2
r
;
a
c
=
r
ω
2
is the most convenient to use.
Solution
Entering the given values of v = 25.0 m/s and r=500 m into the first expression for ac gives
a
c
=
v
2
r
=
(
25.0
m/s
)
2
500
m
=
1.25
m/s
2
a
c
=
v
2
r
=
(
25.0
m/s
)
2
500
m
=
1.25
m/s
2
.
Discussion
To compare this with the acceleration due to gravity (g = 9.80 m/s2), we take the ratio of
a
c
g
=
(
1.25
m/s
2
)
(
9.80
m/s
2
)
=
0.128
a
c
g
=
(
1.25
m/s
2
)
(
9.80
m/s
2
)
=
0.128
. Thus, ac=0.128 g and is noticeable especially if you were not wearing a seat belt.
Explanation:
