Person sitting on scale on roller coaster

[cdornz]

Homework Statement

A 120 pound person is sitting on a scale during a roller coaster ride. As the roller coaster goes over the top of a curve whose radius is 30 feet, the scale indicates a force of 25 pounds. The average speed of the roller coaster doesn't change while over this curve.

A) What forces are acting on the person?
B) Specify the magnitude and direction of each of the forces
C) Draw a free body diagram of the person
D) Describe the acceleration of the person
E) How fast was the roller coaster moving at that time?

Homework Equations

I know that a=mv(squared)/r : This equation goes into the right side of the ƩF=ma.
I know how to draw a free body diagram, start with the object at the center and draw the forces outward.

The Attempt at a Solution

A) I believed the forces to be: Fg=weight of person; Fn=force perpendicular to interface; Ff=mv(squared)/r
B) Fg=120pd, down; Fn=up, don't know magnitude; Ff=(120)v(squared) and I believe this is pointing inward, but I'm kind of confused by that.
C) This I am able to draw if I know the correct direction of the forces.
D) I have no idea how to get the acceleration, but I do have the equation. a=v(squared/r). Problem is, I only have the radius so I don't know how to go about solving for acceleration.
E) This also means I don't understand where to start to figure out the velocity of the roller coaster.

 

[tiny-tim]

welcome to pf!

hi cdornz! welcome to pf!

(try using the X² button just above the Reply box )

A) What forces are acting on the person?
B) Specify the magnitude and direction of each of the forces
C) Draw a free body diagram of the person
D) Describe the acceleration of the person
E) How fast was the roller coaster moving at that time?
…
I know that a=mv(squared)/r : This equation goes into the right side of the ƩF=ma.
…
A) I believed the forces to be: Fg=weight of person; Fn=force perpendicular to interface; Ff=mv(squared)/r

what is "Ff" supposed to be an abbreviation for?

mv²/r is not a force, it's m times acceleration, and as you say, it goes on the RHS of ∑F = ma

B) Fg=120pd, down; Fn=up, don't know magnitude; Ff=(120)v(squared) and I believe this is pointing inward, but I'm kind of confused by that.

yes, you do know the magnitude of Fn: read the question!

(where does Fn come from?)

D) I have no idea how to get the acceleration, but I do have the equation. a=v(squared/r). Problem is, I only have the radius so I don't know how to go about solving for acceleration.

i don't understand … r is the radius

 

[cdornz]

what is "Ff" supposed to be an abbreviation for?

mv²/r is not a force, it's m times acceleration, and as you say, it goes on the RHS of ∑F = ma

yes, you do know the magnitude of Fn: read the question!

(where does Fn come from?)


i don't understand … r is the radius

Ff is supposed to represent force of friction, which I thought there would be since this is technically steel on steel.

As for the magnitude of Fn, would it be 145 pounds? I would assume that is the amount, because that's the amount of force pushing down..I wasn't sure if Fg and Fn would be equal or not.

As for acceleration, radius isn't needed, but I wasn't sure with the correct equation if I could solve for it.

 

[tiny-tim]

Ff is supposed to represent force of friction, which I thought there would be since this is technically steel on steel.

it's rolling … this is a rollercoaster

there's no friction (with the ground or the rail) when something rolls!

(and anyway why would it equal mv²/r ?)

As for the magnitude of Fn, would it be 145 pounds? I would assume that is the amount, because that's the amount of force pushing down..I wasn't sure if Fg and Fn would be equal or not.

why would it be more than the weight?

anyway, what object is this reaction force coming from?

As for acceleration, radius isn't needed, but I wasn't sure with the correct equation if I could solve for it.

i honestly have no idea what you're talking about

what equation do you propose to use for the acceleration?​

 

[Nickie]

I would approach this problem by first identifying all the forces acting on the person, which are gravity (Fg), normal force (Fn), and the centripetal force (Ff). Then, I would use the equations provided and my knowledge of Newton's laws of motion to determine the magnitude and direction of these forces.

To find the acceleration of the person, I would use the equation a=mv^2/r, where m is the mass of the person and v is the velocity of the roller coaster. Since the average speed of the roller coaster does not change during the curve, we can assume that the velocity remains constant and use the given radius to calculate the acceleration.

To find the velocity of the roller coaster, we can use the equation v=√(rg), where r is the radius and g is the acceleration due to gravity. By plugging in the values given, we can find the velocity at that point in the roller coaster ride.

A free body diagram can then be drawn to visually represent the forces acting on the person. The direction of the forces can be determined by the direction in which they are acting.

In conclusion, as a scientist, I would use my knowledge of physics and equations to analyze the situation and find the answers to the questions posed. It is important to approach problems like these with a systematic and analytical mindset to come to a clear and accurate solution.