What is the Linear Speed of an Air Puck in Circular Motion?

In summary, the linear speed of the air puck is determined by equating the tensions and forces acting on the puck and the suspended mass. After solving the equations, the velocity is calculated to be 31.28 m/s, and the combined mass of the two objects is used in the equations.
  • #1
Maiia
79
0

Homework Statement


An air puck of mass 0.029 kg is tied to a string and allowed to revolve in a circle of radius 1.6m on a frictionless horizontal surface. The other end of the string passes through a hole
in the center of the surface, and a mass of 1.4kg is tied to it, as shown in the figure. The
suspended mass remains in equilibrium while the puck revolves on the surface. The acceleration of gravity is 9.81 m/s2 .
What is the linear speed of the puck? answer in m/s.
I got what the forces were- i drew a freebody diagram and had tension and gravity pointing down, with centrifigal acc pointing down as well.
I got tension to be 13.734N and gravity to be .28449N.
I plugged them into Fnet= ma
so T+Fg= m(centrif acc)
thing is, I'm not sure what to use for mass..is it the .029, the combined mass of the two or the mass of the weight on the bottom?
 
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  • #2
Centripetal acceleration=v^2/r
T=(1.4 kg block)*g
T=(mass of small block)(centripetal acceleration) or T=(.029kg)v^2/r

Therefore, (1.4kg)*g=(.029Kg)v^2/r

I think you can take it from there.

With respect to deciding which masses go where: Think about which object*acceleration is supplying the force. The lower object is not spinning and is therefore not contributing to the "spinning force"
 
  • #3
Also, I just noticed: If the object is falling near the surface of Earth the acceleration due to gravity is 9.81m/s^2. Or maybe I didn't understand part of your question.
 
  • #4
Actually the more I look at this,

There are two free body diagrams to draw. The first one is of the block rotating around the table. The second is of the block underneath the table.

From that you will get two equations. Put them together as I did and the rest is algebra.
 
  • #5
hmm i set them equal to each other and i got velocity to be 31.27982714m/s. However, when I submit that, it says I'm wrong...
 
  • #6
That's not what I got for velocity.
(1.4kg)(9.81m/s^2)=(.029Kg)(v^2)/(1.6m)
 
  • #7
ah faulty algebra on my part... Thanks for your help :)
 

FAQ: What is the Linear Speed of an Air Puck in Circular Motion?

How does the air puck maintain its circular motion?

The air puck maintains its circular motion due to the principle of inertia. Inertia is the tendency of an object to maintain its state of motion, whether it is at rest or moving in a straight line. In the case of the air puck, it continues to move in a circular path because there is no external force acting on it to change its direction.

What factors affect the speed of the air puck in circular motion?

The speed of the air puck in circular motion is affected by the radius of the circle, the mass of the puck, and the force applied to keep it in motion. According to Newton's second law of motion, the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass. Therefore, a smaller radius, lighter puck, and stronger force will result in a higher speed.

What happens to the air puck when it reaches the edge of the circular track?

When the air puck reaches the edge of the circular track, it will experience a change in direction due to the normal force exerted by the track. This normal force acts as a centripetal force, pulling the puck towards the center of the circle and keeping it in circular motion. The puck will continue to move in a circular path as long as this force is present.

Can the air puck maintain a constant speed in circular motion?

Yes, the air puck can maintain a constant speed in circular motion as long as the centripetal force remains constant. This means that the force pulling the puck towards the center must be equal to the force pushing it outwards, resulting in a balanced system. Any changes in the force will affect the speed of the puck.

How does friction affect the circular motion of the air puck?

Friction can affect the circular motion of the air puck in two ways. First, it can provide the necessary centripetal force to keep the puck in motion. For example, if the air puck is moving on a rough surface, the friction between the puck and the surface can act as the centripetal force. However, excessive friction can also slow down the puck and cause it to lose its circular motion. Therefore, it is important to minimize friction in order to maintain the desired speed and motion of the air puck.

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