What is the tension in the string for circular motion of keys?

[fa08ti]

Keys with a combined mass of 0.100 kg are attached to a 0.25m long string and swung in a circle in the vertical plane.
a) What is the slowest speed that the keys can swing and still maintain a circular path?
b) What is the tension in the string at the bottom of the circle?


for part a, I used g= v^2/r and rearranged it to v=sqrt(gr)
I got v=2.5 m/s
I'm pretty sure that's right

I think i'd have to use the same equation for the part b?

I'm just stuck on the radius thing for part b
any ideas would be great

 

[Doc Al]

for part a, I used g= v^2/r and rearranged it to v=sqrt(gr)
I got v=2.5 m/s
I'm pretty sure that's right

What did you use for 'r'?

I think i'd have to use the same equation for the part b?

Use Newton's 2nd law.

I'm just stuck on the radius thing for part b

There's only one radius.

 

[fa08ti]

I used 0.25 m...that doesn't seem accurate now

 

[fa08ti]

and isn't the second law F=ma? how would that help since I only know the mass

 

[Doc Al]

I used 0.25 m...that doesn't seem accurate now

Why do you say that?

 

[fa08ti]

well the question said the length of the string is 0.25m. It didn't say the radius was that length. Would I be correct in assuming that the length of the string is the radius?

 

[Doc Al]

and isn't the second law F=ma? how would that help since I only know the mass

You need to identify the forces acting on the keys when they are at the bottom.

What's unclear to me is what speed you're supposed to use at that point. Are you to assume a constant speed as it goes around the circle? (It would naturally pick up speed as it falls.)

 

[Doc Al]

well the question said the length of the string is 0.25m. It didn't say the radius was that length. Would I be correct in assuming that the length of the string is the radius?

Yes. The keys are at the end of the string, thus the string becomes the radius of the circle. (Someone's hand is the center of that circle, presumably.)

 

[fa08ti]

Wouldn't I just use the answer from part a?

 

[Doc Al]

Wouldn't I just use the answer from part a?

I wouldn't think so. The minimum speed is attained at the top; you'd need to figure out the speed at the bottom.

Even part a is a bit ambiguous: Do they want the minimum speed at any point or the minimum speed at the bottom to reach the top?

 

[fa08ti]

It would be at any point

 

[Doc Al]

It would be at any point

Which is what you solved for with the formula you used for part a. (You need to redo your calculation with the correct radius.) The point of minimum speed is at the top of the circle.

 

[fa08ti]

how do i know what the correct radius is?

 

[Doc Al]

how do i know what the correct radius is?

The radius is given; it's the length of the string. (I thought I answered that one.)