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=

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. \[ \theta= \]
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Solution

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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: \[ F_{\text{net}} = \sqrt{(128)^2 + (-172)^2} = \sqrt{16384 + 29584} = \sqrt{45968} \approx 214.4 \mathrm{~N} \]

Final Answer

\[ \boxed{F_{\text{net}} \approx 214.4 \mathrm{~N}} \]

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