---
title: Forces Sample Test Answer Key
date: 2024-09-29
#draft: true
---

> [!faq]- Answer 1
>   $||\vec{F}_N||=9.8*10.0=98\mathrm{N}$, so $0\le||\vec{F}_{fr}||\le\mu_s*98$, where $\mu_s*98=0.4*98=39.2\mathrm{N}$ \
>   A) static friction, $\mu_s=0$ \
>   B) static friction, $\mu_s=10N$ \
>   C) static friction, $20$N is still not sufficient to move the box \
>   D) static friction, $38$N is still not sufficient to move the box, but just barley \
>   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.

> [!faq]- Answer 2 
> $\vec{F}_A=\langle 58, 33.5 \rangle$ in Newtons as a force vector

> [!faq]- Answer 3 
> $F_x$: $28.7$4 N \
> $F_y$: $11.6$1 N \
> $F_{grav}$: $24.5$ N \
> $F_{norm}$: $12.89$ N \
> $F_{net}$: $29 N$, right \
> $a$: $11 \mathrm{m}/\mathrm{s}^2$, right (rounded from $11.497 \mathrm{m}/\mathrm{s}^2$)

> [!faq]- Answer 4 
> $6.8188$ N 

> [!faq]- Answer 5  
> A) $922$ N, B) $1692.91$ N 


> [!faq]- Answer 6 (Part 1)  
> $3.3206$ ms

> [!faq]- Answer 7 (Part 2)  
> 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 $v=?$. $v=0.491874746929 \mathrm{m}/\mathrm{s}$

> [!faq]- Answer 8 (Part 3)  
> $T=25.547907659$, time to hit wall: $\approx\tfrac{T}{2}=12.7739538295$ seconds. 

> [!faq]- Answer 9 
> $5$ N 

> [!faq]- Answer 10 
> $k = 5000$ N/m 

> [!faq]- Answer 11 
> $970 \tfrac{\text{kg}}{\text{m}^3}$

> [!faq]- Answer 12 
> $\eta=22.08333$ ($\eta$ is usually treated as a dimensionless number) (up for debate).

> [!faq]- Answer 13 
> $1350$ N/m
