More on Uniform Circular Motion

[kingwinner]

Circular motion is a new topic for me and I am still struggling through it. I read through the whole chapter on circular motion in my textbook, but still left me with tons of questions. I hope someone can explain and help me out. I know you are all keen physics experts. :Exclamati I really appreciate for your help!

 

1a) A coin is place 15 cm from the axis of a rotating turntable whose rotational frequency can be varied. As the turntable increases its frequency the coin remains on its surface until the turntable reaches 66 revolutions/minute. At the rate, the coin slides off. Find the coefficient of static friction between the coin and the turntable.

[Can I say (coefficient of static friction)(normal force)=4(pi^2)mr(f^2) and then solve for the unknown (coefficient of static friction)? I am having a problem with this method because 4(pi^2)mr(f^2) is the centripetal force NEEDED to keep the coin in circular motion when f=66 revolutions/minute. But in the context of the question, the coin ALREADY slid out.......how can I solve it, then?]

 

 

1b) How would the path followed by the coin as seen by an observer at rest above the turntable look like?

And how would the path followed by the coin as seen by an observer sitting on the turntable exactly at its centre look like?

 

 

2) What minimum speed must a roller coaster be travelling at when upside down at the top of a vertical loop so that the passengers do not fall out? The radius of the loop is 8m.

[The problem is that I don't know how the free body diagram would look like when the passenger is at the top of the loop. Force of gravity is definitely there, but is there any other foce? (normal force?)]

 

 

3) In a "ROTOR-RIDE" at the amusement park, riders are pressed against the inside wall of a vertical cylinder of radius 2.8m. When the ride reaches a rotational speed of 3.2 rad/s, the floor that the passengers are standing drops away. What is the minimum coefficient of friction requried in order that the passengers remain stationary against the wall, and do not slide down?

[Why would the passengers drop away and slide down?

Should I just let the frictional force equal to the centripetal force NEEDED for the passenger to stay in circular motion. I got the answer as 2.9 by doing it this way. This answer seems unreasonable to me, because 2.9 is such a high value for coefficient of friction, so maybe this is not the right approach...]

 

4) A ferris wheel of radius 16m rotates in a vertical circle uniformly once every 20s. What is the "apparent weight" of a 45kg passenger at the highest point of the ride?

[First I would need to know what apparent weight is. My textbook defines "apparent weight" as the net force exerted on an accelerating obejct in a noninertial frame of reference. This wording is too complicated for me to understand.

In simple terms, is "apparent weight" simply the force of gravity on the passenger?]

[Jay-qu]

 

1a) A coin is place 15 cm...

[Can I say (coefficient of static friction)(normal force)=4(pi^2)mr(f^2) and then solve for the unknown (coefficient of static friction)? I am having a problem with this method because 4(pi^2)mr(f^2) is the centripetal force NEEDED to keep the coin in circular motion when f=66 revolutions/minute. But in the context of the question, the coin ALREADY slid out.......how can I solve it, then?]

 

Yes I believe you can say so. You see I find it useless (and some time detrimental) to think of the 'centripetal force' it is the friction that is keeping to thing in circular motion - therefore it is allowed to be equated to (mv^2)/r and then solved.