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)

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

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Short Answer

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Step 1. Given information

Step 2. Explanation

Part (a)

Part (b)

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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

Quantum Physics

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Scientific Method Physics

Study anywhere. Anytime. Across all devices.