Questions: Problem 6: (10% of Assignment Value)
Consider the following three forces:
- F1 = (301 N) i + (467 N) j
- F2 = (-173 N) i
- F3 = (-639 N) j
- Part (a)
What is the x component, in newtons, of the net force?
Fsecx = 128.0 N
✓ Correct!
- Part (b) v
What is the y component, in newtons, of the net force?
- Fsay = -172
- Fseay = -172.0 N
✓ Correct!
- Part (c)
What is the magnitude, in newtons, of the net force?
- Fed = 128 + (-172)
- Fset = -44.00 N X Incorrect! Give Up used.
Part (d)
What is the direction of the net force? Express your answer as the angle which is measured counterclockwise, in degrees, from the positive x axis.
θ=
Transcript text: Problem 6: ( $10 \%$ of Assignment Value)
Consider the following three forces:
\[
\begin{array}{l}
\vec{F}_{1}=(301 \mathrm{~N}) \hat{i}+(467 \mathrm{~N}) \hat{j} \\
\vec{F}_{2}=(-173 \mathrm{~N}) \hat{i} \\
\vec{F}_{3}=(-639 \mathrm{~N}) \hat{j}
\end{array}
\]
- Part (a)
What is the $x$ component, in newtons, of the net force?
\[
F_{\text {secx }}=128.0 \mathrm{~N}
\]
$\checkmark$ Correct!
- Part (b) $\boldsymbol{v}$
What is the $y$ component, in newtons, of the net force?
\[
\begin{array}{l}
F_{\text {say }}=-172 \\
F_{\text {seay }}=-172.0 \mathrm{~N}
\end{array}
\]
$\checkmark$ Correct!
- Part (c)
What is the magnitude, in newtons, of the net force?
\[
\begin{array}{l}
F_{\text {ed }}=128+(-172) \\
F_{\text {set }}=-44.00 \mathrm{~N} \quad \text { X Incorrect! Give Up used. }
\end{array}
\]
Part (d)
What is the direction of the net force? Express your answer as the angle which is measured counterclockwise, in degrees, from the positive $x$ axis.
\[
\theta=
\]
Solution
Solution Steps
Step 1: Calculate the Net Force Components
Given the forces:
\[
\begin{array}{l}
\vec{F}_{1}=(301 \mathrm{~N}) \hat{i}+(467 \mathrm{~N}) \hat{j} \\
\vec{F}_{2}=(-173 \mathrm{~N}) \hat{i} \\
\vec{F}_{3}=(-639 \mathrm{~N}) \hat{j}
\end{array}
\]
The net force components are:
\[
\begin{array}{l}
F_{\text{net},x} = 301 \mathrm{~N} + (-173 \mathrm{~N}) = 128 \mathrm{~N} \\
F_{\text{net},y} = 467 \mathrm{~N} + (-639 \mathrm{~N}) = -172 \mathrm{~N}
\end{array}
\]
Step 2: Calculate the Magnitude of the Net Force
The magnitude of the net force is given by:
\[
F_{\text{net}} = \sqrt{(F_{\text{net},x})^2 + (F_{\text{net},y})^2}
\]
Substituting the values:
\[
F_{\text{net}} = \sqrt{(128)^2 + (-172)^2} = \sqrt{16384 + 29584} = \sqrt{45968} \approx 214.4 \mathrm{~N}
\]