What Speed Keeps the Cylinder Stationary in the Puck-Cylinder System?

In summary, the hanging cylinder will stay at rest if the speed of the puck is equal to the centripetal force (Fc) multiplied by the radius of the cylinder (R).
  • #1
raptik
21
0

Homework Statement


A puck of mass m = 1.10 kg slides in a circle of radius r = 18.0 cm on a frictionless table while attached to a hanging cylinder of mass M = 3.00 kg by a cord through a hole in the table. What speed (in m/s) keeps the cylinder at rest?

Homework Equations


F = ma

The Attempt at a Solution


I know the Fnet,y for the hanging cylinder is zero because it does not move, so I deduced that T - Fg = 0.
On the puck the 2 things I looked at was the a moving towards the hole and the tension which I am also deducing is moving towards the hole, away from the puck. (Note: I left out FN and Fg because I didn't see how they would apply in the equation for the puck.) I thus got the equation T = ma.

I then plugged in the in this T into the previous equation to get: ma - Fg = 0
I then simplified the equation to a = g. Knowing that a in circular motion with constant velocity is a = v2/R, so the equation I ended up with was v = √Rg. This came out to 1.328 ms-1, which is wrong. Could somebody tell me where my thinking went astray and how I can fix this.
 
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  • #2
There are TWO different masses, so you need to keep two different m's in your equation or replace them with the two different numbers. Your solution will be more elegant if you write Fc = Fg first (centripetal force is provided by the gravitational force), then replace them both with their detailed formulas.
 
  • #3
Thank you very much. I overlooked that there were two different masses involved in the equation and just worked them out of my problem by mistake.
 
  • #4
Most welcome! It is a pleasure to save you the frustration of a tiny mistake after you demonstrate your mastery of the whole problem.
 

Related to What Speed Keeps the Cylinder Stationary in the Puck-Cylinder System?

1. What is centrifugal force?

Centrifugal force is a fictitious force that appears to act on an object moving in a circular path. It is a result of the object's inertia trying to keep it moving in a straight line.

2. How does the centrifugal force of a puck affect its movement?

The centrifugal force of a puck causes it to move in a curved path, as it tries to maintain its momentum while being pushed towards the center of the circular path.

3. How do you calculate the centrifugal force of a puck?

The centrifugal force of a puck can be calculated using the formula Fc = mv^2/r, where m is the mass of the puck, v is its velocity, and r is the radius of the circular path.

4. Is centrifugal force a real force?

No, centrifugal force is not a real force. It is a result of the object's inertia and the centripetal force acting on it.

5. How does the mass and velocity of a puck affect its centrifugal force?

The greater the mass and velocity of a puck, the greater its centrifugal force will be. This means that a heavier and faster moving puck will require a stronger centripetal force to keep it in a circular path.

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