Rotational Motion and Coefficient of Friction

In summary: Then use that information to find the acceleration (in terms of a vector) of each body.In summary, Tajivie is looking for help solving a physics problem from a previous test. He starts by sketching out what he is seeing, and then calculates the forces acting on each body.
  • #1
tajivie
4
0
Hey guys!
Ok, so I don't have that much to work with, and I am sorry for my lack of detail, but my memory is a bit fuzzy. I had to do a problem like this for my physics test yesturday:

On the test we were given a problem involving a roller coaster (Rotating Drum of Death was its name). Essentially we were given the radius (for the design of the ride was that of a sphere) and the rotational speed in radians per second. In the problem, the floor of the ride dropped out and but the people on board did not fall to their deaths below because there was a coefficient of friction keeping them inside the ride. The question was to solve for the coefficient of friction. (There was no mass given) Can you please help me solve this problem?

Expereince Info:
This was part of a chapter concerning Rotational Motion. I know how to calculate coefficients of friction when an object is moving down an incline plane, but I have no idea how to solve this problem (also, it was short answer response so there are infinite options)!
 
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  • #2
Did you draw a force diagram for the person on the ride?
 
  • #3
Villyer said:
Did you draw a force diagram for the person on the ride?

Yes, I was able to draw a diagram :) My problem though is calculating the coefficient of friction. I believe the radius was 12m and the rotational speed was approx. 8rad/s
 
  • #4
Hi tajivie! It is customary to post a question only once in the forumhttps://www.physicsforums.com/images/icons/icon4.gif [Broken] I've copied my response in your duplicate thread over to this one. Can you ask for the other one to be deleted?

It has taken me 10 mins of pondering all possibilities before I figured out what this refers to. Misnaming it "rollercoaster" led me way off track to start with.
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Okay, you recognize the arrangement they are talking about? So start out with a sketch that helps you determine, for each body, the steady centripetal force pressing it towards the centre of rotation.
 
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  • #5


Hi there,

I can help you with this problem. The first step in solving this problem is to define the forces acting on the people inside the roller coaster. In this case, there are two main forces at play: the centripetal force, which keeps the people moving in a circular motion, and the frictional force, which prevents them from sliding out of the ride.

To solve for the coefficient of friction, we can use the equation:

μ = Ff/Fn

Where μ is the coefficient of friction, Ff is the frictional force, and Fn is the normal force (in this case, the weight of the people).

To calculate the frictional force, we can use the equation:

Ff = μN

Where N is the normal force, which is equal to the weight of the people in this case.

To calculate the centripetal force, we can use the equation:

Fc = mv^2/r

Where m is the mass of the people, v is the rotational speed in radians per second, and r is the radius of the ride.

Now, we can substitute these equations into the first equation to solve for μ. Keep in mind that the normal force is equal to the weight of the people, so we can substitute this value into the equation as well.

μ = Ff/Fn = μN/mg = (mv^2/r)/mg = v^2/rg

Therefore, the coefficient of friction is equal to the square of the rotational speed divided by the product of the radius and acceleration due to gravity.

I hope this helps you solve the problem. Let me know if you have any further questions!
 

What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. This type of motion can occur in circular, elliptical, or other curved paths. It is described by parameters such as angular velocity, angular acceleration, and moment of inertia.

What is the coefficient of friction?

The coefficient of friction is a value that represents the amount of resistance between two surfaces in contact. It is a dimensionless quantity and is typically denoted by the symbol "μ". A higher coefficient of friction means there is more resistance between the surfaces, while a lower coefficient of friction means there is less resistance.

How is rotational motion related to coefficient of friction?

In rotational motion, the coefficient of friction plays a role in determining the amount of torque required to overcome the resistance between two surfaces. This resistance is what allows an object to rotate around an axis. The coefficient of friction also affects the speed and stability of rotational motion.

How do you calculate the coefficient of friction?

The coefficient of friction can be calculated by dividing the force of friction by the normal force between two surfaces. This can be expressed as μ = Ff/Fn, where μ is the coefficient of friction, Ff is the force of friction, and Fn is the normal force. The coefficient of friction can also be determined experimentally by measuring the force needed to move an object along a surface.

What factors affect the coefficient of friction?

The coefficient of friction can be affected by several factors, including the nature of the surfaces in contact, the smoothness of the surfaces, the presence of any lubricants or contaminants, and the amount of force applied to the surfaces. Additionally, the coefficient of friction can vary depending on the type of motion (e.g. sliding, rolling, or spinning) and the temperature of the surfaces.

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