Calculating Velocity of 100g Mass to Describe Circle on Table

In summary, the conversation discusses a problem involving a 100-gram mass attached to a string passing through a hole in a table and supporting a 200-gram mass. The question is asking for the velocity needed to project the 100-gram mass in a circular path with a radius of 25cm on the table. The solution involves considering the centripetal force required to keep the mass moving in a circular path and the weight of the other mass at the other end of the string. Friction is not a factor in this problem as the table is assumed to be smooth. The use of free body diagrams is recommended to better understand the forces acting on each mass.
  • #1
Procrastinate
158
0
A particle of mass 100grams rests on a smooth horizontal table and is attached to one end of a string which passes through a small hole in the table and supports a particle of 200grams. With what velocity must the 100gram mass be projected on the table so as to describe on the table a circle of radius 25cm.

I am wondering whether anyone could give me a hint?

I am confused as to what to do with both a 100gram mass and a 200gram mass.
 
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  • #2
Okay, here's a hint: what centripetal force is required to keep the top mass moving on a circular path? What is providing that centripetal force?
 
  • #3
Draw a free-body diagram of what is happening.

If the 200g mass is hanging, what is its weight?
 
  • #4
cepheid said:
Okay, here's a hint: what centripetal force is required to keep the top mass moving on a circular path? What is providing that centripetal force?

It would be friction wouldn't it? Without friction, there wouldn't be centripetal force.
 
  • #5
rock.freak667 said:
Draw a free-body diagram of what is happening.

If the 200g mass is hanging, what is its weight?

It would be 1.96. I drew a diagram and it just looks like a mass attached to a string which leads to the usual conical motion diagram.

I think it has something to do with the tension of the first string that holds onto the second mass.
 
  • #6
Procrastinate said:
It would be friction wouldn't it? Without friction, there wouldn't be centripetal force.

No. When the problem says the mass rests on a "smooth" table, that should be interpreted as the table having negligible friction.

It's the force on the mass due to the tension in the string that provides the centripetal force. Think about what would happen if the string broke (or if the tension were to otherwise disappear). Would the particle move in a circular path any more?

So that raises the question, what's keeping the string taut, and what determines by how much it pulls on the tabletop mass? The answer to both questions is: "the weight of the other mass at the other end of the string."

Procrastinate said:
It would be 1.96.

1.96 WHAT? Such statements are meaningless without units.

Procrastinate said:
I drew a diagram and it just looks like a mass attached to a string which leads to the usual conical motion diagram.

What do you mean the usual "conical motion diagram?" Besides, rock.freak667 asked you to draw a free body diagram. Do you know what that is? It means you isolate one body in the system and draw ONLY that, as well as the forces acting upon it. You do not draw any other parts of the system that aren't that body. That's why it's called a FREE body diagram. Therefore, you'd need a separate free body diagram for each mass. It's tremendously useful to take inventory of the forces that should be acting on each mass in this way. Try again, and let us know how it goes.
 

FAQ: Calculating Velocity of 100g Mass to Describe Circle on Table

How do you calculate the velocity of a 100g mass to describe a circle on a table?

To calculate the velocity of a 100g mass, you need to know the mass, radius of the circle, and the time it takes to complete one full revolution. Use the formula v = 2πr/t, where v is velocity, π is pi, r is the radius, and t is the time. Plug in the values and solve for velocity.

Do you need to use any specific units in the velocity formula?

Yes, it is important to use consistent units in the velocity formula. The mass should be in grams, the radius in meters, and the time in seconds. This will ensure that the velocity is calculated accurately.

How does the mass of the object affect the velocity?

The mass of an object does not directly affect its velocity in circular motion. However, a larger mass may require more force to maintain a circular path, which can affect the velocity. In the formula, the mass is used to calculate the centripetal force needed to keep the object in circular motion.

Can you use this formula for objects of any size?

Yes, this formula can be used for objects of any size as long as the mass, radius, and time are known. However, it may not accurately describe the motion of very small or very large objects due to other factors such as air resistance or gravitational pull.

Is there any other information needed to accurately describe the motion of the object?

In addition to the mass, radius, and time, you may also need to consider any external forces acting on the object, such as friction or gravity. These forces can affect the velocity and should be taken into account for a more accurate description of the motion.

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