purse

logistic_guy

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A 2.0\displaystyle 2.0-kg\displaystyle \text{kg} purse is dropped 55 m\displaystyle 55 \ \text{m} from the top of the Leaning Tower of Pisa\displaystyle \text{Leaning Tower of Pisa} and reaches the ground with a speed of 29 m/s\displaystyle 29 \ \text{m/s}. What was the average force of air resistance?
 
A 2.0\displaystyle 2.0-kg\displaystyle \text{kg} purse is dropped 55 m\displaystyle 55 \ \text{m} from the top of the Leaning Tower of Pisa\displaystyle \text{Leaning Tower of Pisa} and reaches the ground with a speed of 29 m/s\displaystyle 29 \ \text{m/s}. What was the average force of air resistance?
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A 2.0\displaystyle 2.0-kg\displaystyle \text{kg} purse is dropped 55 m\displaystyle 55 \ \text{m} from the top of the Leaning Tower of Pisa\displaystyle \text{Leaning Tower of Pisa} and reaches the ground with a speed of 29 m/s\displaystyle 29 \ \text{m/s}. What was the average force of air resistance?
Simple Newton force equation.

mgFA=ma\displaystyle mg - F_A = ma

We have two unknowns, but if we assume that the acceleration a\displaystyle a is constant, we can calculate it from this equation:

v2=v02+2ay\displaystyle v^2 = v^2_0 + 2ay

a=v2v022y\displaystyle a = \frac{v^2 - v^2_0}{2y}

This gives:

mgFA=mv2v022y\displaystyle mg - F_A = m\frac{v^2 - v^2_0}{2y}

Or

FA=mgmv22y=m(gv22y)\displaystyle F_A = mg - m\frac{v^2}{2y} = m\left(g - \frac{v^2}{2y}\right) since v0=0\displaystyle v_0 = 0.

Plug in numbers.

FA=2(9.82922(55))=4.31 N\displaystyle F_A = 2\left(9.8 - \frac{29^2}{2(55)}\right) = \textcolor{blue}{4.31 \ \text{N}}
 
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