Q65P A purse at radius 2.00 m 聽and a... [FREE SOLUTION]

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Chapter 4: Q65P (page 88)

A purse at radius 2.00 m and a wallet at radius 3.00 m travel in uniform circular motion on the floor of a merry-go-round as the ride turns. They are on the same radial line. At one instant, the acceleration of the purse is $(2.00 m / s^{2}) \hat{i} + (4.00 m / s^{2}) \hat{j}$ .At that instant and in unit-vector notation, what is the acceleration of the wallet?

Short Answer

Expert verified

The acceleration of the wallet is ${\overset{鈫�}{a}}_{w} = (3.00 m / s^{2}) \hat{i} + (6.00 m / s^{2}) \hat{j}$

Step by step solution

Given

The radius of the purse is $r_{p} = 2.00 m$
The radius of the wallet is $r_{w} = 3.00 m$

The acceleration of the purse is, $a = (2.00 m / s^{2}) \hat{i} + (4.00 m / s^{2}) \hat{j}$

Understanding the concept of circular motion

A purse and wallet travel in a uniform circular motion. They are on the same radial line; hence the angular frequency of the purse and wallet is the same. Both have centripetal acceleration only.

Formula:

$a = 蝇^{2} r$

Calculate the acceleration of the wallet

The purse and the wallet are performing uniform circular motion. The radius of purse - $r_{P}$ and radius of the wallet - $r_{w}$ are acting along the same line; hence their angular velocity isthesame.

The equation of acceleration of purse is

$a_{P} = 蝇^{2} r_{P}$ 鈥�(颈)

The equation of acceleration of wallet is

$a_{w} = 蝇^{2} r_{w}$ 鈥�(颈颈)

Dividing equation (ii) by (i),

$\frac{a_{w}}{a_{p}} = \frac{r_{w}}{r_{p}} a_{w} = \frac{r_{w}}{r_{p}} a_{w} \overset{鈫�}{a_{w}} = \frac{3}{2} ((2.00 m / s^{2}) \hat{i} + (4.00 m / s^{2}) \hat{j}) = (3.00 m / s^{2}) \hat{i} + (6.00 m / s^{2}) \hat{j}$