Find the Friction (Rotational Problem)

  • Thread starter Thread starter proximaankit
  • Start date Start date
  • Tags Tags
    Friction
AI Thread Summary
The problem involves a hula-hoop with a mass of 500g and a radius of 55 cm, launched vertically and sliding on a wooden basketball court before rolling without slipping after 20 m. The key equations relate torque, frictional force, and acceleration, but confusion arises from using the same symbols for different variables. The friction is responsible for the hoop's rotation and deceleration during the sliding phase. The condition for rolling without slipping is crucial, as it indicates a relationship between linear and angular acceleration. Understanding the transition from slipping to rolling is essential for determining the coefficient of kinetic friction.
proximaankit
Messages
11
Reaction score
0

Homework Statement


One afternoon, you are playing on a wooden basketball court with a hula‐hoop to amuse yourself. The hoop has a mass of 500g and a radius of 55 cm. After practicing a bit, you find that you can launch the hoop so that its plane is vertical, it isn’t rotating before it hits the floor, and it doesn’t bounce after hitting the floor. For these launch conditions, the hoop’s CM moves initially with a speed of 3 m/s along the floor. You notice that as the hoop slips along the floor it begins to rotate, and that just before it hits the far wall 20 m away from the launch point, it “catches” and begins to roll without slipping. What is the coefficient of kinetic friction between the hoop and the floor?


Homework Equations


τ=Iα=f*r where f is frictional force
f=μmg
f=ma
I = MR^2

The Attempt at a Solution


Tried various method to solve for μ, but it ends up canceling itself. i.e.:
f*r=MR^2*(a/r)
a=f/M
f =f/M
 
Physics news on Phys.org
Please show your reasoning.
Notice that the hoop slides for a while before it "catches" - what is happening in this part of the motion?
What is the condition for rolling without slipping?
 
proximaankit said:
τ=Iα=f*r where f is frictional force
f=μmg
f=ma
I = MR^2

The Attempt at a Solution


Tried various method to solve for μ, but it ends up canceling itself. i.e.:
f*r=MR^2*(a/r)
a=f/M
f =f/M
It's rather hard to follow if you keep using the same symbol (f) to mean different things. Please define all your variables and name them uniquely.
 
Sorry for the confusion but here is what I was trying to do
At the bottom of the hoop, as the hoop starts to rotate, that must mean that friction is causing the rotation. In my free body diagram I had. friction to left of point of contact and Normal up and weight down. Friction acting on the object cause it rotate so it will have angular acceleration. Friction cause the hoop to have acceleration since it should be slowing down. so f (friction ) = ma. By torque eqn. τ=f*l=Iα=MR^2(a/r) -> which arrives to the same equation of f = ma. And from here I am lost.
 
proximaankit said:
Sorry for the confusion but here is what I was trying to do
At the bottom of the hoop, as the hoop starts to rotate, that must mean that friction is causing the rotation. In my free body diagram I had. friction to left of point of contact and Normal up and weight down. Friction acting on the object cause it rotate so it will have angular acceleration. Friction cause the hoop to have acceleration since it should be slowing down. so f (friction ) = ma. By torque eqn. τ=f*l=Iα=MR^2(a/r) -> which arrives to the same equation of f = ma. And from here I am lost.
You got the same equation because you assumed αr = a. But you can only be sure of that once it is rolling. So these equations are telling you something you didn't know, that αr = a holds even while it is slipping. But it might not be terribly useful.
Think about velocity. You are given the initial linear and rotational velocities, and a relationship between the final velocities.
 
Thread 'Struggling to make relation between elastic force and height'
Hello guys this is what I tried so far. I used the UTS to calculate the force it needs when the rope tears. My idea was to make a relationship/ function that would give me the force depending on height. Yeah i couldnt find a way to solve it. I also thought about how I could use hooks law (how it was given to me in my script) with the thought of instead of having two part of a rope id have one singular rope from the middle to the top where I could find the difference in height. But the...
Thread 'Voltmeter readings for this circuit with switches'
TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...

Similar threads

Back
Top