Mass on a rotating turntable problem.

In summary, the conversation discusses the calculation of the speed and time required for a block to remain in circular motion on a turntable. The FBD of the block is analyzed, with the normal force equaling its weight in the y coordinates and static friction to the left and a centripetal force to the right in the x coordinates. The outside observer must provide a centripetal force to hold the block in circular motion, which is calculated using Fc = Ff. Finally, the speed of the turntable, omega*R, is determined as the necessary speed for the block to remain in circular motion.
  • #1
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[PLAIN]http://img841.imageshack.us/img841/7913/314pw.jpg [Broken]

I'm having a bit of trouble with this one.

So the FBD of the block.

In the y coordinates, the normal equals its weight

in the x coordinates, we have static friction to the left, and is there a force to the right? There as to be right, since it eventually begins translating radially?

Just looking for a little guidance, thanks!
 
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  • #2
From the point of view of the outside observer, a centripetal force is required to hold the mass in circular motion. This is provided by the force of friction. So you begin with Fc = Ff, put in the details and calculate the speed for which they are just equal.
 
  • #3
the speed of the turntable and the block or just equal?

omega*R?
 
  • #4
Yes, the speed of the turntable omega*R.
Then you can go for the time to reach that speed.
 
  • #5


I would suggest approaching this problem by first identifying all the forces acting on the block. In the y direction, the normal force and weight are equal and opposite, so they cancel out. In the x direction, there is a static friction force acting to the left, which is necessary to prevent the block from sliding off the turntable.

As the turntable rotates, the block experiences a centrifugal force directed outward from the center of rotation. This force is responsible for the block's eventual translation radially. In order for the block to remain in equilibrium, there must also be a force acting in the opposite direction, towards the center of rotation. This force is provided by the static friction force, which adjusts its direction to always point towards the center of rotation.

In summary, the block experiences a normal force and a static friction force in the x direction, and a centrifugal force in the radial direction. These forces work together to keep the block in equilibrium on the rotating turntable.
 

1. What is the Coriolis effect and how does it affect the mass on a rotating turntable problem?

The Coriolis effect is a phenomenon that occurs when a mass is moving in a rotating reference frame. It causes the mass to appear to deviate from a straight path, and instead follow a curved path. In the context of a rotating turntable, the Coriolis effect causes the mass to experience a force that is perpendicular to its motion, which can cause it to move towards the center of the turntable.

2. How does the mass on a rotating turntable problem relate to the concept of inertia?

The mass on a rotating turntable problem is a good example of inertia, which is the tendency of an object to resist changes in its state of motion. In this problem, the mass wants to continue moving in a straight line, but the rotation of the turntable causes it to follow a curved path. This demonstrates how inertia can cause objects to behave differently in different reference frames.

3. What is the role of centripetal force in the mass on a rotating turntable problem?

Centripetal force is the force that acts towards the center of a circular path. In the context of a rotating turntable, the centripetal force is provided by the tension in the string that is holding the mass in place. This force is necessary to keep the mass moving in a circular path, as it constantly wants to move in a straight line due to its inertia.

4. How does the mass affect the behavior of the rotating turntable in this problem?

The mass on the rotating turntable affects its behavior in several ways. Firstly, the mass provides the centripetal force that keeps the turntable rotating at a constant speed. Additionally, the mass also experiences a centrifugal force, which is equal and opposite to the centripetal force. This force can cause the turntable to wobble or tilt slightly as the mass moves in a circular path.

5. Can the mass on a rotating turntable problem be applied to real-life situations?

Yes, the mass on a rotating turntable problem is a simplified version of many real-life situations where a rotating reference frame is involved. For example, it can be used to understand the motion of objects on a merry-go-round, or the behavior of hurricanes and other weather systems. It is also relevant in fields such as engineering, physics, and meteorology.

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