Centripetal force question -- car speed on an offramp

[Dorthea]

Homework Statement

If a car doubles its speed on a circular off-ramp how much more centripetal force will be required for it to make the turn2. The attempt at a solution
I think that half of the centripetal force will be required for it to make the turn due to the fact that faster the car goes, the lower the centripetal force. Is this correct? Thanks in advance!

 

[berkeman]

Homework Statement

If a car doubles its speed on a circular off-ramp how much more centripetal force will be required for it to make the turn2. The attempt at a solution
I think that half of the centripetal force will be required for it to make the turn due to the fact that faster the car goes, the lower the centripetal force. Is this correct? Thanks in advance!

Welcome to the PF.

Please write out the equations involved for centripetal acceleration versus linear and angular speed. Base your answer on those equations, and give a quantitative answer (how much more or less...?).

 

[SammyS]

Homework Statement

If a car doubles its speed on a circular off-ramp how much more centripetal force will be required for it to make the turn2. The attempt at a solution
I think that half of the centripetal force will be required for it to make the turn due to the fact that faster the car goes, the lower the centripetal force. Is this correct? Thanks in advance!

Hello Dorthea. Welcome to PF.

Please explain your answer further.

How is centripetal acceleration related to speed and the radius of the circular off-ramp?

 

[Dorthea]

How is centripetal acceleration related to speed and the radius of the circular off-ramp?

Centripetal acceleration is directly related to the speed and inversely related to the radius of the off ramp

 

[SammyS]

Centripetal acceleration is directly related to the speed and inversely related to the radius of the off ramp

Not quite right .

Do you have a formula for this?

 

[Dorthea]

Is the formula Ac=v²/r?

 

[SammyS]

Is the formula Ac=v²/r?

That's right.

So the centripetal force is directly proportional to the square of the speed and inversely proportional to the radius.

Now, can you answer the original question in post #1?

 

[Dorthea]

Now, can you answer the original question in post #1?

This is an application question for a lab, so we aren't given actual values and I'm just going to use hypothetical values.
Say the original speed is 10 m/s, which would be doubled to equal 20 m/s and the radius is 10m.

The centripetal acceleration for the first speed would be 10²/10 which equals 10m/s²
The centripetal acceleration for the second speed would be 20²/10 which equals 40m/s²

Thus, 4 times the centripetal force will be required for it to make the turn.

 

[SammyS]

This is an application question for a lab, so we aren't given actual values and I'm just going to use hypothetical values.
Say the original speed is 10 m/s, which would be doubled to equal 20 m/s and the radius is 10m.

The centripetal acceleration for the first speed would be 10²/10 which equals 10m/s²
The centripetal acceleration for the second speed would be 20²/10 which equals 40m/s²

Thus, 4 times the centripetal force will be required for it to make the turn?

Right.

Of course you can come to the same conclusion using only the information in post #1, without plugging in specific numbers.

 

[Dorthea]

Right.

Of course you can come to the same conclusion using only the information in post #1, without plugging in specific numbers.

Ohh ok. Thank you so much for helping me understand this question!