On Earth, the maximum speed without
skidding for a car on a level circular
curved track of radius 40m is 15m/s. This
car and track are then transported to
another planet for the Indy Galactic 500.
The Maximum speed is 8.4m/s. What is
the value of the acceleration due to gravity
on this other planet?
40 m
What are we looking for?
The key to solving this problem is to find the
coefficient of friction between the car and
the surface of the planet it’s on (denoted
by μ). This will be the same for on Earth as
well as at the Indy Galactic 500
How do we find μ?
Take note that the centripetal force acting on
the car is friction. Therefore:
F(centripetal) = F(friction)
Here’s where some Algebra kicks
in:
F(centripetal)
=
F(c) = (mass)(acceleration)
F(Friction)
F(f) = μF(normal)
=μF(gravity)
= ma
=μ(mass)(gravity)
=μmg
The masses on
either side
cancel out and
we end up with
this formula.
We’ll use it later:
ma = μmg
a = μg
Acceleration = μ(gravity)
So Now We’re on Earth
First, let’s find the acceleration of the car
using this formula: a = v^2 / r
r = 40 m
v = 15 m/s
15^2 / 40 = 5.625 m/s/s
Now we find μ
Remember this formula?
a = μg
It can also be rewritten to this:
μ = a/g
We know that:
a = 5.625 and
g on planet earth is approx. 9.8
μ = a/g
μ = 5.625/9.8
μ = 0.57
Yaaaay, we found μ! Now we can travel
to that other planet and find out it’s
acceleration due to gravity!
Welcome to the Indy Galactic
500
First thing’s first, we need to find the
acceleration of the car on this mystery
planet using the same formula we used on
earth.
v = 8.4m/s
a = 8.4^2/40 = 1.764m/s/s
r = 40m
Remember: a = μg
a = 1.746m/s/s
μ = 0.57
Therefore:
1.746 = 0.57(gravity)
Divide both sides by 0.57 and we get:
The Answer:
Acceleration due to
gravity = 3.09m/s/s