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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 18 / Problem 70P

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Answer: Insect Collisions. A cubical cage 1.25 m on each

Chapter 18, Problem 70P

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QUESTION:

Problem 70P

Insect Collisions. A cubical cage 1.25 m on each side contains 2500 angry bees, each flying randomly at 1.10 m/s. We can model these insects as spheres 1.50 cm in diameter. On the average, (a) how far does a typical bee travel between collisions, (b) what is the average time between collisions, and (c) how many collisions per second does a bee make?

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QUESTION:

Problem 70P

Insect Collisions. A cubical cage 1.25 m on each side contains 2500 angry bees, each flying randomly at 1.10 m/s. We can model these insects as spheres 1.50 cm in diameter. On the average, (a) how far does a typical bee travel between collisions, (b) what is the average time between collisions, and (c) how many collisions per second does a bee make?

ANSWER:

Solution 70P

Step 1:

Data given

Length on side of cubical cage $V=\ (1.25\ m{)}^{3}\$

Number of bees $N=\ 2500$

Velocity of bees $v=\ 1.10\ m/s$

Diameter of sphere = $d=\ 1.50\ cm\$

Thus we have $r=\ 0.75\ cm\$

Consider

$\lambda{}=\ v{t}_{mean}=\ \frac{V}{4π\ \sqrt{2}{r}^{2}N\ }$

Substituting the values we get

$\lambda{}=\ \frac{(1.25\ m{)}^{3}}{4π\ \sqrt{2}\times{}(0.75\ \times{}1{0}^{-2}m\ {)}^{2}2500\ }\$

$\lambda{}=\ \frac{(1.25\ m{)}^{3}}{24991.21}\$

$\lambda{}=\ 7.81\times{}1{0}^{-3\ }m\ =\ 7.80\ cm\$

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