Chapter 3: Q. 44 (page 79)

Four forces are exerted on the object shown in FIGURE P3.44. (Forces are measured in newtons, abbreviated N.) The net force on the object is ${\vec{F}}_{net} = {\vec{F}}_{1} + {\vec{F}}_{2} + {\vec{F}}_{3} + {\vec{F}}_{4} = 4.0 \hat{ı} N$ . What are (a) ${\vec{F}}_{3}$ and (b) ${\vec{F}}_{4}$ ? Give your answers in component form.

Short Answer

Expert verified

The forces $F_{3}$ and $F_{4}$ are ${\vec{F}}_{3} = (2.9 N) \hat{j}$ and ${\vec{F}}_{4} = (1.64 N) \hat{i}$

Step by step solution

Step 1. Given information

The net force

${\vec{F}}_{n e t} = {\vec{F}}_{1} + {\vec{F}}_{2} + {\vec{F}}_{3} + {\vec{F}}_{4} = 4 \hat{i}$

Step 2. Explanation

If a vector F is inclined by an angle $θ$ with respect to the x- axis, and the x-component is $F \cos θ$ and its y - component is $F \sin θ$ .

Resolving $F_{2}$ into two components, along x-axis and along the y-axis as shown in the following figure:

$\begin{array}{l} {\vec{F}}_{n e t} = {\vec{F}}_{1} + {\vec{F}}_{2} + {\vec{F}}_{3} + {\vec{F}}_{4} 4 \hat{i} + 0 \hat{j} \\ {\vec{F}}_{n e t} = [5 (- \hat{j})] + [6 \cos 20^{°} \hat{i} + 6 \sin 20^{°} \hat{j}] + F_{3} \hat{j} + [F_{4} (- \hat{i})] 4 \hat{i} + 0 \hat{j} \\ 4 \hat{i} = (6 \cos 20^{°} - F_{4}) \hat{i} + (6 \sin 20^{°} + F_{3} - 5) \hat{j} ..... (1) \end{array}$

Part (a)

Comparing both y-component of expression (1)

$\begin{array}{l} 0 \hat{j} = (6 \sin 20^{°} + F_{3} - 5) \hat{j} \\ \Rightarrow {\vec{F}}_{3} = (2.9 N) \hat{j} \end{array}$

Part (b)

Comparing x-component of expression (1)

$\begin{array}{l} 4 \hat{i} = (6 \cos 20^{°} - F_{4}) \hat{i} \\ {\vec{F}}_{4} = (6 \cos 20^{°} - 4) \hat{i} \\ {\vec{F}}_{4} = (1.64 N) \hat{i} \end{array}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

Part (a)

Part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Electricity and Magnetism

Force

Geometrical and Physical Optics

Conservation of Energy and Momentum

Fluids

Study anywhere. Anytime. Across all devices.

Four forces are exerted on the object shown in FIGURE P3.44. (Forces are measured in newtons, abbreviated N.) The net force on the object isF→net=F→1+F→2+F→3+F→4=4.0ı^N . What are (a)F→3 and (b) F→4? Give your answers in component form.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

Part (a)

Part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Electricity and Magnetism

Force

Geometrical and Physical Optics

Conservation of Energy and Momentum

Fluids

Study anywhere. Anytime. Across all devices.