Chapter 5: Q8P (page 116)

$2.00 k g$ the object is subjected to three forces that give it an acceleration $\vec{a} = - (8.00 m / s^{2}) \hat{i} + (6.00 m / s^{2}) \hat{j}$ . If two of the three forces are role="math" localid="1656998692451" $\vec{F_{1}} = (30.0 N) \hat{i} + (16.0 N) \hat{j}$ and $\vec{F_{2}} = - (12.0 N) \hat{i} + (8.0 N) \hat{j}$ find the third force.

Short Answer

Expert verified

The third force is $(- 36 N) \hat{i} + (- 12 N) \hat{j}$

Step by step solution

The given data

Object of mass, $m = 2.00 k g$ .
Acceleration of object, $\vec{a} = (- 8.00 m / s^{2}) \hat{i} + (6.00 m / s^{2}) \hat{j}$ .
Two forces are given,localid="1657001038844" $\vec{F_{1}} = (30 N) \hat{i} + (16 N) \hat{j} & \vec{F_{2}} = (- 12.0 N) \hat{i} + (8.00 N) \hat{j}$ .

Understanding the concept of Newton’s second law

If there is more than one force acting on the body, then the net force is found by vector addition of the object. Newton’s law gives the relation between the net force ${\vec{F}}_{N e t}$ on a body with a mass m and the body’s acceleration as,

${\vec{F}}_{N e t} = m \vec{a}$ (i)

Using the formula for Newton’s second law, we can find the third force.

Calculation of third force

From equation (i), we have the net force as follows:

${\vec{F}}_{N e t} = \vec{F_{1}} + \vec{F_{2}} + \vec{F_{3}} m \vec{a} = \vec{F_{1}} + \vec{F_{2}} + \vec{F_{3}} \vec{F_{3}} = m \vec{a} - \vec{F_{1}} - \vec{F_{2}}$

Substitute the values of mass, acceleration, and two forces to calculate the third force.

$\vec{F_{3}} = 2.00 k g [(- 8.00 m / s^{2}) \hat{i} + (6.00 m / s) \hat{j}] - [(30 N) \hat{i} + (16 N) \hat{j}] - [(- 12.0 N) \hat{i} + (8.00 N) \hat{j}] = (- 34 N) \hat{i} + (- 12 N) \hat{j}$

Hence, the third force is

(- 34 N) \hat{i} + (- 12 N) \hat{j}

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Short Answer

Step by step solution

The given data

Understanding the concept of Newton’s second law

Calculation of third force

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2.00kg the object is subjected to three forces that give it an acceleration a→=-(8.00m/s2)i^+(6.00m/s2)j^ . If two of the three forces are role="math" localid="1656998692451" F1→=(30.0N)i^+(16.0N)j^ andF2→=-(12.0N)i^+(8.0N)j^ find the third force.

Short Answer

Step by step solution

The given data

Understanding the concept of Newton’s second law

Calculation of third force

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Astrophysics

Electrostatics

Fields in Physics

Physics of Motion

Thermodynamics

Study anywhere. Anytime. Across all devices.