Centripetal Force: What Happens When Force Increases?

[Mohamad]

Suppose, there is an object in a circular path that goes with a cirtain speed. What happens, if suddenly the centripetal force increases?
a) The object remains in the path but its speed increases
b) The object exits the circular path
c) Any other situation
Please, explain your answer, thanks

 

[haushofer]

Please, explain your own thoughts first, thanks

 

[haushofer]

But to give you a hint: first write down the formula and see which quantities are involved.

 

[Mohamad]

I think, I explained my thoughts, I think maybe one of the (a) or (b) situation occurs, but I'm not sure. Which part of the question is vague?

 

[Mohamad]

But to give you a hint: first write down the formula and see which quantities are involved.

I only know a=v^2/r. So, should I conclude that when the force increases the acceleration increases as well and
a) The object remains in the path but its speed increases
is correct?

 

[A.T.]

Suppose, there is an object in a circular path that goes with a cirtain speed. What happens, if suddenly the centripetal force increases?

How is "centripetal" defined here?
1) Towards a fixed center (central force)?
2) Always perpendicular to velocity (normal force)?

 

[Mohamad]

How is "centripetal" defined here?
1) Towards a fixed center (central force)?
2) Always perpendicular to velocity (normal force)?

1) Towards a fixed center (central force)

 

[A.T.]

1) Towards a fixed center (central force)?

In a=v^2/r the a is perpendicular to v, not necessarily towards a fixed center.

 

[PeroK]

I think, I explained my thoughts, I think maybe one of the (a) or (b) situation occurs, but I'm not sure. Which part of the question is vague?

What would happen if you are swinging an object round in a circle using a string and you pull the string harder?

 

[A.T.]

What would happen if you are swinging an object round in a circle using a string and you pull the string harder?

@Mohamad To visualize this better, imagine m₂ is such that m₁ is on a circular path, and then you increase m₂ suddenly.

Image from:
https://www.khanacademy.org/science...entripetal-forces/a/what-is-centripetal-force

 

[Mohamad]

In a=v^2/r the a is perpendicular to v, not necessarily towards a fixed center.

I thought when path is a circle, a is perpendicular to v. Is this wrong?

 

[A.T.]

I thought when path is a circle...

You want to find the path, not assume it.

What do you think happens if you suddenly increase m₂ in post #10?

 

[Mohamad]

You want to find the path, not assume it.

What do you think happens if you suddenly increase m₂ in post #10?

A.T. F=mrω², m is consntant, r could not increase, so I think ω should increase.
Do I hava a misconception?
P.S. a is perpendicular to v so I used that formula.

 

[PeroK]

F=mrω², m is consntant, r could not increase, so I think ω should increase.
Do I hava a misconception?

Yes, you have a misconception. Imagine a ball was moving in a circle and the additional centripetal force was provided by a bat, hitting the ball in the direction of the centre. Why would the ball speed up in its orbit and not be propelled out of its orbit?

 

[Mohamad]

Yes, you have a misconception. Imagine a ball was moving in a circle and the additional centripetal force was provided by a bat, hitting the ball in the direction of the centre. Why would the ball speed up in its orbit and not be propelled out of its orbit?

OK, so if extra force propelled out the ball, how we can increase the speed of an object when we are swinging an object round in a circle using a string?

 

[PeroK]

OK, so if extra force propelled out the ball, how we can increase the speed of an object when we are swinging an object round in a circle using a string?

Once the ball has left its original circular path, the force is no longer perpendicular to its motion. The ball speeds up.

What happens depends on how you manoeuvre the string. The ball could spiral into a smaller circular orbit. Or, by letting the string back out the ball can be manoeuvred into the original orbit (radius) at higher speed and higher tension in the string.

This process can be repeated to make the ball go faster and faster.

PS technically, to do this you have to pull the string slightly off-centre to increase the angular momentum about the central point.

If the force is always strictly centripetal then AM is conserved and the radius of the motion must reduce if the ball speeds up.

PPS in other contexts, such as planetary orbits, you might end up with an elliptical orbit if there is a change in the centripetal force. For example, you could transition from a powered circular orbit to a natural elliptical.orbit by cutting the engines.

 

[A.T.]

r could not increase

What about decrease?

a is perpendicular to v so I used that formula.

You said that F & a are always towards a fixed center, not that they are always perpendicular to v. While in uniform circular motion there is no difference between the two possibilities, but you don't know what the motion will be when the force increases.

 

[A.T.]

...how we can increase the speed of an object when we are swinging an object round in a circle using a string?

We cannot if the hand is fixed at the center and the string is fixed in the hand.

 

[rcgldr]

I have images for the two cases mentioned above. If the force is towards a fixed point, such as the string going through a hole, then the energy increases as the string is pulled downwards through the hole, and the energy decreases if the string is allowed to move upwards through the hole. Angular momentum is conserved. in the "hole" image below, the short lines show the direction of force, which is not perpendicular to the path (so the energy and speed change).



If the string wraps around a post, the force is always centripetal (perpendicular to current velocity), energy remains constant, and angular momentum is not conserved unless you include the momentum of whatever the post is attached to (such as eventually the earth), since there's a torque on the post.

 

[Mister T]

I thought when path is a circle, a is perpendicular to v. Is this wrong?

That's right. But it can also be true when the path is not a circle.

 

[Mohamad]

If the force is always strictly centripetal then AM is conserved

Can I conclude that in this video, if the curve be circle, the car can't increase its speed in the curve?
And if this is true what happens if the driver press the gas pedal more?

 

[A.T.]

Can I conclude that in this video, if the curve is circle, the car can't increase its speed in the curve?

It can.

... what happens if the driver press the gas pedal more?

The force is not strictly centripetal.