Chapter 12: Q87P (page 353)

A particle is acted on by forces given, in newtons, by $\vec{F_{1}} = 8 .40 \hat{i} - 5 .70 \hat{j}$ and $\vec{F_{2}} = 16 .0 \hat{i} + 4 .10 \hat{j}$ . (a) What are the xcomponent $\vec{F_{3}}$ and (b) ycomponent of the force Fthat balances the sum of these forces? (c) What angle does $\vec{F_{3}}$ have relative to the $+ x a x i s$ ?

Short Answer

Expert verified

a) the x component of force F₃, $F_{x} = - 24.4$ .

b) y component of force F₃, $F_{y} = 1.60$ .

c) The angle of force F₃ with the +x axis, $θ = - 3.75 °$ .

Step by step solution

Understanding the given information

$\vec{F_{1}} = 8.40 - 5.70$

$\vec{F_{2}} = 16.0 + 4.10$

Step 2: Concept and formula used in the given question

Using the equation of equilibrium of force, you can find the components of force F₃ and its angle. The formulas are given below.

$\begin{array}{l} {\vec{F}}_{n e t} = \vec{F_{1}} + \vec{F_{2}} \\ θ = (\frac{F_{y}}{F_{x}}) \end{array}$

(a) Calculation for thex component F3→

The net force acting on the particle is given by,

${\vec{F}}_{n e t} = \vec{F_{1}} + \vec{F_{2}}$

So, $\vec{F_{n e t}} = 24.4 \hat{i} - 1.60 \hat{j}$

Hence, the force $\vec{F_{3}}$ which balances the force $\vec{F_{net}}$ can be written as,

$\vec{F_{3}} = - 24.4 \hat{i} + 1.60 \hat{j}$

From the equation of $\vec{F_{3}}$ ,we get the x component as,

$F_{x} = - 24.4 N$

(b) Calculation for they component of the force F that balances the sum of these forces

From the equation of $\vec{F_{3}}$ you get the y component as,

$F_{y} = 1.60 N$

(c) Calculation for theangle does F3→ have relative to the +x-axis

The angle of the force $\vec{F_{3}}$ can be calculated using the equation,

$\begin{matrix} θ = (\frac{F_{y}}{F_{x}}) \\ = (\frac{1.60 N}{- 24.2 N}) \\ = - 3.75 ° \end{matrix}$

The negative sign implies that the angle is measured in the clockwise direction with respect to the positive x-axis.

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Short Answer

Step by step solution

Understanding the given information

Step 2: Concept and formula used in the given question

(a) Calculation for thex component F3→

(b) Calculation for they component of the force F that balances the sum of these forces

(c) Calculation for theangle does F3→ have relative to the +x-axis

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A particle is acted on by forces given, in newtons, by F1→=8.40i^−5.70j^and F2→=16.0i^+4.10j^ . (a) What are the xcomponentF3→ and (b) ycomponent of the force Fthat balances the sum of these forces? (c) What angle does F3→have relative to the+xaxis ?

Short Answer

Step by step solution

Understanding the given information

Step 2: Concept and formula used in the given question

(a) Calculation for thex component F3→

(b) Calculation for they component of the force F that balances the sum of these forces

(c) Calculation for theangle does F3→ have relative to the +x-axis

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Nuclear Physics

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Circular Motion and Gravitation

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Study anywhere. Anytime. Across all devices.