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- Homework Statement
- Keys with a combined mass of 0.100 kg are attached to a 0.25 m long string and swung in a circle in the vertical plane.

a)Determine the slowest speed that the keys can swing and still maintain a circular path.

b)Determine the magnitude of the tension in the string at the bottom of the circle.

- Relevant Equations
- Fnet = Fg+ Ft

Fc = Fg + Ft

Fc= mv^2 / r

Fg = mg

a)Determine the slowest speed that the keys can swing and still maintain a circular path.

Fnet = Fg + Ft

Fc = Fg + Ft

When Ft = 0, Fc = Fg

So, Fc = mv^2 / r and Fg = mg

mv^2/r = mg

v = √gr

v = √9.81 * 0.25

v = 1.56 m/s

Therefore, the slowest speed that the keys can swing and still maintain a circular path is 1.56m/s.

b) Determine the magnitude of the tension in the string at the bottom of the circle.

In order to determine the magnitude of the tension in the string at the bottom of the circle I would need to find the minimum speed at the bottom of the circle. How can I find that? I know that I need to include velocity from part a, but not sure what else to do.

Fnet = Fg + Ft

Fc = Fg + Ft

When Ft = 0, Fc = Fg

So, Fc = mv^2 / r and Fg = mg

mv^2/r = mg

v = √gr

v = √9.81 * 0.25

v = 1.56 m/s

Therefore, the slowest speed that the keys can swing and still maintain a circular path is 1.56m/s.

b) Determine the magnitude of the tension in the string at the bottom of the circle.

In order to determine the magnitude of the tension in the string at the bottom of the circle I would need to find the minimum speed at the bottom of the circle. How can I find that? I know that I need to include velocity from part a, but not sure what else to do.