Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

An object is tracked by a radar station and determined to have a position vector given by $\vec{r} = (3500 - 160 t) \hat{i} + 2700 \hat{j} + 300 \hat{k}, with \vec{r}$ in meters and t in seconds. The radar station’s x axis points east, its y axis north, and its z axis vertically up. If the object is a 250 kg meteorological missile, what are (a) its linear momentum, (b) its direction of motion, and (c) the net force on it?

a) The linear momentum of an object is $(- 4.0 \times 10^{4} kg . \frac{m}{s}) \hat{i}$ .

b) The direction of motion of the object is along the negative x-axis.

c) The net force on the object is 0.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Listing the given quantities

The mass of an object is, $m = 250 kg$ .

The position vector of the object, $\vec{r} = (3500 - 160 t) \hat{i} + 2700 \hat{j} + 300 \hat{k}$ .

Step 2: Understanding the concept of the law of conservation of momentum

Here, we can apply the calculus knowledge along with Newton’s second law of motion.

Formula:

$\vec{v} = \frac{d \vec{r}}{d t} \vec{P} = m \vec{v}$

Step 3: (a) Calculation of linear momentum

The equation for velocity is,

$\vec{v} = \frac{d \vec{r}}{d t}$

Substitute the values in the above expression, and we get,

$\vec{v} = \frac{d ((3500 - 160 t) \hat{i} + 2700 \hat{j} + 300 \hat{k})}{d t} = - 160 \hat{i}$

Linear momentum can be calculated as,

$\vec{P} = m \vec{v}$

Substitute the values in the above expression, and we get,

$\vec{P} = 250 \times (- 160 \hat{i}) = (- 4.0 \times 10^{4} kg . \frac{m}{s})$

Thus, the linear momentum of an object, $\vec{P} = (- 4.0 \times 10^{4} kg . \frac{m}{s})$ .

Step 4: (b) Direction of motion

From the equation of velocity, we can say that the direction of motion of the object is (- x) direction.

Thus, the direction of motion is in the -x (west) direction .

Step 5: (c) Calculation of net force

The equation of force in terms of momentum is,

$\vec{F} = \frac{d \vec{P}}{d t}$

From part a, since the value of P does not change with time, we get,

$\vec{F} = 0$

Thus, the net force on the object, $\vec{F} = 0$

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Listing the given quantities

Step 2: Understanding the concept of the law of conservation of momentum

Step 3: (a) Calculation of linear momentum

Step 4: (b) Direction of motion

Step 5: (c) Calculation of net force

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Fundamentals Of Physics

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Step by Step Solution

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Step 3: (a) Calculation of linear momentum

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Step 5: (c) Calculation of net force

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