Mass spinning on table; connected to dangling mass

In summary, the purpose of mass spinning on a table connected to a dangling mass is to demonstrate rotational motion and the effects of different masses on a system. The spinning mass creates a centripetal force that pulls the dangling mass towards the center of rotation, causing it to move in a circular motion. Factors such as the mass of the spinning object, distance from the center of rotation, and force applied can affect the speed of the spinning mass. There is a limit to how fast the mass can spin, determined by the strength of materials and applied force. The length of the string connecting the spinning and dangling masses affects the rotation by changing the radius and speed of rotation.
  • #1
unscientific
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Homework Statement


oh1cg9.png





The Attempt at a Solution



7 Part(a)
It can be seen that Eα > Emin, so ue is always bounded below Eα.
2eg5vtw.png


7 Part (b)
It can be seen that for α = 1/2, Eα = Emin = -1/4. Thus for α < 1/2, the mass will start to drop.
2gwt6xt.png


What puzzles me is how do you explain this using forces?

Force acting on mass on table = T
Force acting on mass below = mg - T

The mass would slide down if mg > T but how do i express this in terms of α??
 
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  • #2



it is important to approach this problem using a scientific and systematic approach. Let's start by defining some variables and equations that will help us understand the situation better.

First, let's define the force of gravity as Fg = mg, where m is the mass of the object and g is the acceleration due to gravity. Next, let's define the tension force as T, which is the force applied by the string to the object.

Now, let's look at the forces acting on the object when it is hanging from the string. The only force acting on the object is the force of gravity, Fg. This force is balanced by the tension force, T, which keeps the object in equilibrium.

When we change the angle α, we are essentially changing the direction of the force of gravity. As α decreases, the force of gravity becomes more horizontal and less vertical. This means that the component of the force of gravity acting perpendicular to the table decreases, while the component acting parallel to the table increases.

Now, let's consider the forces acting on the object when it is resting on the table. The force of gravity, Fg, is still acting on the object, but now there is also a normal force, Fn, acting on the object from the table. This normal force is equal in magnitude and opposite in direction to the component of the force of gravity acting perpendicular to the table.

Using this information, we can now express the condition for the object to slide down the table in terms of α. For the object to slide down, the force of gravity acting parallel to the table must be greater than the frictional force, which is equal to the normal force, Fn. In other words, mg sinα > μFn, where μ is the coefficient of friction between the object and the table.

We can also express this condition in terms of the tension force, T. Remember that T is equal to the force of gravity acting parallel to the table, so we can rewrite the condition as T > μFn.

In summary, as α decreases, the component of the force of gravity acting parallel to the table increases, making it more likely for the object to slide down. This can be expressed in terms of the tension force, T, as T > μFn. I hope this explanation helps to clarify the relationship between forces and the angle α in this situation.
 

1. What is the purpose of mass spinning on a table connected to a dangling mass?

The purpose of this experiment is to demonstrate the concept of rotational motion and the effects of different masses on the rotation of a system.

2. How does the mass spinning on the table affect the dangling mass?

The spinning mass on the table creates a force called centripetal force, which pulls the dangling mass towards the center of rotation. This causes the dangling mass to move in a circular motion.

3. What factors can affect the speed of the mass spinning on the table?

The speed of the spinning mass can be affected by the mass of the spinning object, the distance between the spinning mass and the center of rotation, and the force applied to spin the mass.

4. Is there a limit to how fast the mass can spin on the table?

Yes, there is a limit to how fast the mass can spin on the table. This is determined by the strength of the materials used and the force applied to spin the mass. If the speed exceeds this limit, the spinning mass may break or fly off the table.

5. How does the length of the string connecting the spinning mass to the dangling mass affect the rotation?

The length of the string affects the distance between the spinning mass and the center of rotation, which in turn affects the speed and direction of rotation. A shorter string will result in a smaller radius of rotation and a faster rotation speed, while a longer string will result in a larger radius of rotation and a slower rotation speed.

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