Motion in a plane II, Coin on a turntable with Vmax

In summary, the conversation discussed the problem of determining the maximum angular velocity at which a turntable can spin without a coin sliding on its surface. Through analyzing the forces acting on the coin and using equations for maximum velocity and angular velocity, the solution of 8.09 rad/s was calculated.
  • #1
SherBear
81
0

Homework Statement



A 3.90 g coin is placed 12.0cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of Ws= 0.800 and Wk= 0.410.

What is the maximum angular velocity with which the turntable can spin without the coin sliding?



Homework Equations


?



The Attempt at a Solution


? no idea
can you please show all the steps and the solution, thank you!
 
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  • #2
Draw a free body diagram of the coin showing all forces. Then look at the forces and determine how they interact with one another.
 
  • #3
LawrenceC said:
Draw a free body diagram of the coin showing all forces. Then look at the forces and determine how they interact with one another.

Does a turntable turn clockwise? Normal force up, mg down, Ff opposite of the motion if clockwise then it's counterclock wise?

I have Vmax=SQRT Ws r g=SQRT .800*.12m*9.81 m/s^2= .938 m/s, but I don't know if that's a relevant equation.

Then I have an equation for angular velocity=Vt=wr
 
  • #4
SherBear said:
Does a turntable turn clockwise? Normal force up, mg down, Ff opposite of the motion if clockwise then it's counterclock wise?



The turntable is turning at constant speed so you are not concerned with tangential force here. We want to determine what the maximum speed is.

At the point of impending coin movement outward, what forces are exactly balanced?
 
  • #5
"I have Vmax=SQRT Ws r g=SQRT .800*.12m*9.81 m/s^2= .938 m/s"

Use parentheses.

Your calculator seems to cause problems.

I am signing off for the day. You are on the right track.

Angular velocity = V/r
 
Last edited:
  • #6
LawrenceC said:
The turntable is turning at constant speed so you are not concerned with tangential force here. We want to determine what the maximum speed is.

At the point of impending coin movement outward, what forces are exactly balanced?

I think the normal force and gravitational forced are the balanced forces.
 
  • #7
ok i did the calc with para, and the result was Vmax=.9704 m/s
then i plugged that into the m=v/r
.9704 m/s / .12 m = 8.09 rad/s ?
 
  • #8
That is what I calculated. Good work.
 
  • #9
Thank you Lawrence! and for all your help and hardwork also! :)
 

FAQ: Motion in a plane II, Coin on a turntable with Vmax

1. What is the relationship between the velocity of a coin on a turntable and its maximum velocity?

The velocity of a coin on a turntable is directly proportional to its maximum velocity. This means that as the velocity of the coin increases, its maximum velocity also increases.

2. How does the radius of the turntable affect the motion of the coin?

The radius of the turntable has a significant influence on the motion of the coin. As the radius increases, the coin will have a larger circular path and a higher maximum velocity. Conversely, a smaller radius will result in a smaller circular path and a lower maximum velocity.

3. How does the mass of the coin affect its motion on the turntable?

The mass of the coin does not have a direct effect on its motion on the turntable. However, a heavier coin may require more force to maintain a constant velocity, resulting in a decrease in maximum velocity.

4. Does the speed of the turntable affect the motion of the coin?

Yes, the speed of the turntable has a direct impact on the motion of the coin. A faster turntable will result in a higher maximum velocity of the coin, while a slower turntable will result in a lower maximum velocity.

5. How does the angle of the turntable affect the trajectory of the coin?

The angle of the turntable has a significant influence on the trajectory of the coin. A steeper angle will result in a more elliptical path, while a shallower angle will result in a more circular path. This will also affect the maximum velocity of the coin, with a steeper angle resulting in a higher maximum velocity.

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