# Centripetal force while a car makes a turn

#### greenrichy

Problem Statement
A pair of fuzzy dice is hanging by a string from the rearview window. While making a right turn at 60 mph, the fuzzy dice makes an angle of 23 degrees from the vertical.
(1) Determine the radius of the circular path of the fuzzy dice.
(2) What is the mechanical force acting as the centripetal force on the following entities:
(a) - The fuzzy dice
(b) - The car
(c) - The driver
Relevant Equations
None
Correct me if I'm wrong, but I think it is not possible to solve (1) with all the data that's given.

As for (2), I have come up with the following solutions:
(a) - The tension in the string acts as the centripetal force on the fuzzy dice
(b) - The frictional force between the road and the car
(c) - None?

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#### CWatters

Homework Helper
Gold Member
Correct me if I'm wrong, but I think it is not possible to solve (1) with all the data that's given.
It is. Start with a free body diagram. Write some equations. Some things cancel.

#### CWatters

Homework Helper
Gold Member
As for (2), I have come up with the following solutions:
(a) - The tension in the string acts as the centripetal force on the fuzzy dice
(b) - The frictional force between the road and the car
(c) - None?
(a) I would say it's the horizontal component of the string tension.
(b) Correct
(c) Are you sure? Does the driver move in a straight line?

#### greenrichy

It is. Start with a free body diagram. Write some equations. Some things cancel.
Thanks for your reply. From a free body diagram of FD (Fuzzy dice), I know that we can find the centripetal acceleration, right? But how do I find the tangential velocity?

Last edited:

#### haruspex

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Gold Member
2018 Award
how do I find the tangential velocity?
How is the velocity you are given not the tangential velocity?

#### greenrichy

How is the velocity you are given not the tangential velocity?
So the tangential velocity with which the dice swing is the same as the car's velocity?

#### haruspex

Homework Helper
Gold Member
2018 Award
So the tangential velocity with which the dice swing is the same as the car's velocity?
Depending exactly on where the dice are laterally within the car and how long the string is, the two speeds are unlikely to be exactly the same, but near enough. It is clear you are expected to take them as the same, but well spotted that they need not be.

#### greenrichy

Depending exactly on where the dice are laterally within the car and how long the string is, the two speeds are unlikely to be exactly the same, but near enough. It is clear you are expected to take them as the same, but well spotted that they need not be.
So I found that the centripetal acceleration is equal to 4.2 m/s^2. Given all the data that I have, the radius of the circular path of the dice turns out to be 171.3 meters. I calculated it using this formula --> a = v^2/r.

Does it look right?

#### haruspex

Homework Helper
Gold Member
2018 Award
So I found that the centripetal acceleration is equal to 4.2 m/s^2. Given all the data that I have, the radius of the circular path of the dice turns out to be 171.3 meters. I calculated it using this formula --> a = v^2/r.

Does it look right?
That’s about right. I get slightly more. Did you plug in the acceleration as exactly 4.2? That would introduce a rounding error... better to do the entire calculation in your calculator with no intermediate rounding.
Anyway, you are quoting too many sig figs given the input data.

#### greenrichy

That’s about right. I get slightly more. Did you plug in the acceleration as exactly 4.2? That would introduce a rounding error... better to do the entire calculation in your calculator with no intermediate rounding.
Anyway, you are quoting too many sig figs given the input data.
Got it, that makes sense. Thank you for your help.

"Centripetal force while a car makes a turn"

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