Calculating Velocity of 100g Mass to Describe Circle on Table

[Procrastinate]

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.

 

[cepheid]

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?

 

[rock.freak667]

Draw a free-body diagram of what is happening.

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

 

[Procrastinate]

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.

 

[Procrastinate]

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.

 

[cepheid]

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."

It would be 1.96.

1.96 WHAT? Such statements are meaningless without units.

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.