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Chapter 4: Q. 35 (page 107)

35. II Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the pebble's speed and acceleration?

Short Answer

Expert verified

The speed of pebble is $5.652 m / s$

The acceleration of the pebble is $106.48 m / s^{2}$

Step by step solution

01

Step 1. Given information

The diameter of the wheel is $60 cm$ , the pebble stuck in the thread goes by three times every second.

02

Step 2. Explanation

The speed of the pebble is,

$v = (\frac{d}{2}) 蝇$

The angular velocity of the pebble is

- $蝇 = 2 蟺 N$

Here, $N$ is the revolution per second.

Substitute $3 rev / s$ for $N$ in the above equation to find $蝇$ .

$蝇 = 2 蟺 (3 rev / s) = 18.84 rad / s$ Conclusion:

Substitute $18.84 rad / s$ for $蝇$ and $60 cm$ for $d$ in the equation (I) to find $v$ .

$v = (\frac{(60 cm 脳 \frac{1 m}{100 cm})}{2}) (18.84 rad / s) = 5.652 m / s$

The acceleration of the pebble is,

$a = \frac{v^{2}}{(\frac{d}{2})}$

Here, $d$ is the diameter of the wheel, and $v$ is the speed of the pebble.

$a = \frac{{(5.652 m / s)}^{2}}{(\frac{60 cm 脳 \frac{1 m}{100 cm}}{2})}$

$\begin{array}{l} = \frac{2 脳 100 脳 {(5.652 m / s)}^{2}}{60 m} \\ = 106.48 m / s^{2} \end{array}$

Thus, the acceleration of the pebble is $106.48 m / s^{2}$ .

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