A few questions from an already graded test on classical forces

[cwbullivant]

Homework Statement

A mass m is suspended from a spinning rod by two massless cords of equal length L, held fixed at points along the rod D meters apart. It is observed that m moves in a circle with a tangential velocity v, find the ratio of the tensions between the two supporting cords

Homework Equations

Newton's three laws of motion

The Attempt at a Solution

I didn't get terribly far on this one; I focused too much time on frictional forces during study.

I set up the problem, showing an isoceles triangle pointing rightward (with the mass m at the nexus), and angles θ₁ and θ₂. I didn't get too much farther due to time constraints while actually taking the test, and the instructor himself won't be available to answer it for close to a week. Any help is appreciated.

I can post an image of what I did once I get home, in case it helps.

 

[SammyS]

Homework Statement

A mass m is suspended from a spinning rod by two massless cords of equal length L, held fixed at points along the rod D meters apart. It is observed that m moves in a circle with a tangential velocity v, find the ratio of the tensions between the two supporting cords

Homework Equations

Newton's three laws of motion

The Attempt at a Solution

I didn't get terribly far on this one; I focused too much time on frictional forces during study.

I set up the problem, showing an isoceles triangle pointing rightward (with the mass m at the nexus), and angles θ₁ and θ₂. I didn't get too much farther due to time constraints while actually taking the test, and the instructor himself won't be available to answer it for close to a week. Any help is appreciated.

I can post an image of what I did once I get home, in case it helps.

Do you have a figure you can post or can you describe the situation in more detail?

 

[haruspex]

I assume the rod is vertical. It would have been nicer of the questioner to make that clear, particularly since 'suspended' makes it sound otherwise.
Why did you put two different angles?
Make up some variable names for the two tensions and see what equations you can write down for the vertical and horizontal forces and accelerations.

 

[cwbullivant]

I assume the rod is vertical. It would have been nicer of the questioner to make that clear, particularly since 'suspended' makes it sound otherwise.
Why did you put two different angles?
Make up some variable names for the two tensions and see what equations you can write down for the vertical and horizontal forces and accelerations.

Ok, here's the image with picture.

I wrote down two angles, thinking that I needed to find a ratio of the angles first. Seems to be rather poor reasoning in hindsight.

 

[SammyS]

Ok, here's the image with picture.

I wrote down two angles, thinking that I needed to find a ratio of the angles first. Seems to be rather poor reasoning in hindsight.

For an isosceles triangle, θ₁ = θ₂. Right?

 

[cwbullivant]

For an isosceles triangle, θ₁ = θ₂. Right?

In that case, because θ₁ = θ₂ and L₁ = L₂, would the tensions be equal, and thus in a 1:1 ratio?

 

[SammyS]

In that case, because θ₁ = θ₂ and L₁ = L₂, would the tensions be equal, and thus in a 1:1 ratio?

No. the tensions would not be equal.

Draw a free body diagram for the mass, m.