- #1

Specter

## Homework Statement

Question:

Keys combined with a combined mass of 0.100 kg are attached to a 0.25 m long string swung 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 a the circle?

We are given:

m = 0.100 kg

r = 0.25 m

We need:

v

_{minimum}

## Homework Equations

Fc = mv

^{2}/r

Fg = mg

## The Attempt at a Solution

My solution for

**part a**which I think is correct:

Fc=mv

^{2}/r

mg = mv

^{2}/r

g = v

^{2}/r

v^2 = g*r

v^2 = sqrt(9.8)(0.25)

v = 1.564 rounded 1.57 m/s.

Part b attempts:

I was told on another website to use conservation of energy but I haven't been taught that yet.

**Attempt #1:**

Fc = mv

^{2}/r

Ft - mg = mv

^{2}/r

Ft - (0.100)(9.8) = (0.100)(1.57)

^{2}/0.25

Ft = 0.98 + 0.628

Ft = 1.608

**Attempt #2:**

Fc = mv

^{2}/r

Ft-Fg = mv

^{2}/r

Ft-mg = mv

^{2}/r

Ft-g = v

^{2}/r

Ft = v

^{2}/gr

Ft = 1.57

^{2}/(9.8)(0.25)

Ft = 1.0 N

**Attempt #3:**

Fc = mv

^{2}/r

Ft -mg = mv

^{2}/r

Ft = mv

^{2}/r + mg

Ft = (0.100)(1.57)

^{2}/(0.25) + (0.100)(9.8)

Ft = 1.965 rounded to 2.0 N

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