Vertical loop problem

[Hippo89]

Homework Statement

Whats’s the minimum speed so that car stays in contact with the top of a vertical loop? R = 9.7 m, mass of car = 257 kg

Relevant Equations

Fc = MAc

I got the answer right, but it involved some guessing. So I’m here to make sure I got a conceptual understanding of this.

Normal force is a contact force. If the car was not in contact with the loop (or barely in contact), the loop would exert no normal force on the car. So at the minimum speed, the car would have minimum contact with the loop at the top, meaning that the loop would exert 0 Normal force on The car At the top.

Fcar, top = MAc = W = MG. Ac = G. 9.8 = (min speed)^2/9.7.

Vmin = 9.75 m/s for the car to keep in contact with loop of R = 9.7 m.

 

[erobz]

Homework Statement:: Whats’s the minimum speed so that car stays in contact with the top of a vertical loop? R = 9.7 m, mass of car = 257 kg
Relevant Equations:: Fc = MAc

I got the answer right, but it involved some guessing. So I’m here to make sure I got a conceptual understanding of this.

Normal force is a contact force. If the car was not in contact with the loop (or barely in contact), the loop would exert no normal force on the car. So at the minimum speed, the car would have minimum contact with the loop at the top, meaning that the loop would exert 0 Normal force on The car At the top.

Fcar, top = MAc = W = MG. Ac = G. 9.8 = (min speed)^2/9.7.

Vmin = 9.75 m/s for the car to keep in contact with loop of R = 9.7 m.

Side note: You should be worried about the minimum speed needed at the bottom of the loop if the fictious car were going to have a chance at making the loop.

 

[kuruman]

Homework Statement:: Whats’s the minimum speed so that car stays in contact with the top of a vertical loop? R = 9.7 m, mass of car = 257 kg
Relevant Equations:: Fc = MAc

I got the answer right, but it involved some guessing. So I’m here to make sure I got a conceptual understanding of this.

I am not saying that your solution is wrong, but here you wondering if it is right. The way to do it convincingly "right" is to write Newton's second law equation in the general case where the normal force $N$ is not zero. Then set $N=0$ in that equation and see what you get for the speed. Follow this procedure for this particular problem and you will see why your answer came out right.

Side note: You should be worried about the minimum speed you need at the bottom of the loop if you are performing the stunt.

I wouldn't perform the stunt going at minimum speed at the bottom. In fact, I would step heavily on the accelerator to make sure I have more than enough speed at the top to keep the normal force nonzero.

 

[erobz]

I wouldn't perform the stunt going at minimum speed at the bottom. In fact, I would step heavily on the accelerator to make sure I have more than enough speed at the top to keep the normal force nonzero.

What...are you 🐔?

 

[kuruman]

What...are you 🐔?

That I am. Seriously though, one has has to be careful with what one writes in these forums. A numbskull looking for a challenge above and beyond the idiotic Tik-Tok challenges might actually decide to try this, thinking that it's OK because "the physics geeks at PF" said or implied so. I am too 🐔 to want that kind of responsibility, even if the chances are remote, hence the disclaimer.

 

[erobz]

That I am. Seriously though, one has has to be careful with what one writes in these forums. A numbskull looking for a challenge above and beyond the idiotic Tik-Tok challenges might actually decide to try this, thinking that it's OK because "the physics geeks at PF" said or implied so. I am too 🐔 to want that kind of responsibility, even if the chances are remote, hence the disclaimer.

Well, how about we just stick to marbles on hot wheels track! I edited the wording of the post.

 

[haruspex]

Well, how about we just stick to marbles on hot wheels track! I edited the wording of the post.

Would a marble need the same speed at the bottom that a car would ?

 

[erobz]

Would a marble need the same speed at the bottom that a car would ?

My gut says no...I think it would depend on how idealized we make the analysis though?

I'm not sure what you are getting at. I was saying lets go with marbles, because of what @kuruman said about people trying to do this stunt; not because I thought a marble on a hot wheels track was an equivalent model to a car.