56 lines
1.8 KiB
Markdown
56 lines
1.8 KiB
Markdown
---
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title: Forces Sample Test Answer Key
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date: 2024-09-29
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#draft: true
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---
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> [!faq]- Answer 1
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> $||\vec{F}_N||=9.8*10.0=98\mathrm{N}$, so $0\le||\vec{F}_{fr}||\le\mu_s*98$, where $\mu_s*98=0.4*98=39.2\mathrm{N}$ \
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> A) static friction, $\mu_s=0$ \
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> B) static friction, $\mu_s=10N$ \
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> C) static friction, $20$N is still not sufficient to move the box \
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> D) static friction, $38$N is still not sufficient to move the box, but just barley \
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> E) kinetic friction, $40\mathrm{N}>39.2\mathrm{N}$, $||\vec{F}_{fr}||=0.30*98\mathrm{N}=29.4\mathrm{N}$. $40\mathrm{N}-29.4\mathrm{N}=10.6\mathrm{N}$, to see how fast the box will move: $\frac{||\vec{F}_f||}{10.0\mathrm{kg}}=1.06$ m/s. In freedom units: $2.371152$ Miles an hour.
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> [!faq]- Answer 2
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> $\vec{F}_A=\langle 58, 33.5 \rangle$ in Newtons as a force vector
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> [!faq]- Answer 3
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> $F_x$: $28.7$4 N \
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> $F_y$: $11.6$1 N \
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> $F_{grav}$: $24.5$ N \
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> $F_{norm}$: $12.89$ N \
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> $F_{net}$: $29 N$, right \
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> $a$: $11 \mathrm{m}/\mathrm{s}^2$, right (rounded from $11.497 \mathrm{m}/\mathrm{s}^2$)
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> [!faq]- Answer 4
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> $6.8188$ N
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> [!faq]- Answer 5
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> A) $922$ N, B) $1692.91$ N
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> [!faq]- Answer 6 (Part 1)
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> $3.3206$ ms
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> [!faq]- Answer 7 (Part 2)
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> mass of the door: $61.2244897959$ kg, using the momentum equation: $p_1=p_2=1*v(3.3206\mathrm{ms)=61.2244897959*v})$, and you need to solve for $v=?$. $v=0.491874746929 \mathrm{m}/\mathrm{s}$
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> [!faq]- Answer 8 (Part 3)
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> $T=25.547907659$, time to hit wall: $\approx\tfrac{T}{2}=12.7739538295$ seconds.
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> [!faq]- Answer 9
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> $5$ N
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> [!faq]- Answer 10
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> $k = 5000$ N/m
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> [!faq]- Answer 11
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> $970 \tfrac{\text{kg}}{\text{m}^3}$
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> [!faq]- Answer 12
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> $\eta=22.08333$ ($\eta$ is usually treated as a dimensionless number) (up for debate).
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> [!faq]- Answer 13
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> $1350$ N/m
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