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content/physics/forces-test/forces-answer-key.md Normal file
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---
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
> $10.6$ N
> [!faq]- Answer 5
> A) $942$ N, B) $846$ 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
> $\eta=2.18$ ($\eta$ is usually treated as a dimensionless number).
> [!faq]- Answer 13
> $1350$ N/m

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---
date: 2024-09-29
title: Forces Sample Test Paper
---
> [!IMPORTANT]
> The entirety of the sample test will be of the FRQ format.
All necessary material can be found [here](Forces)
> [!NOTE] Question 1
> *Friction: static and kinetic.* A $10.0$ kg mystery box rests on a horizontal floor. The coefficient of static friction is $\mu_s=0.40$ and the coefficient of kinetic friction is $\mu_k=0.30$ Determine the force of friction $\vec{F}_{fr}$, acting on the box if a horizontal external applied force $\vec{F}_A$ is exerted on it of a magnitude: \
> A) 0 \
> B) 10N \
> C) 20N \
> D) 38N \
> E) 40N
> [!NOTE] Question 2
> Hector is walking his dog (Fido) around the neighborhood. Upon arriving at Fidella's house (a friend of Fido's), Fido turns part mule and refuses to continue on the walk. Hector yanks on the chain with a $67.0$ N force at an angle of $30.0\degree$ above the horizontal. Determine the horizontal and vertical components of the tension force in vector form.
> [!NOTE] Question 3
> Lee Mealone is sledding with his friends. Disgruntled by a coarse comment, he decides to separate from the group. He momentarily exerts a 31 N force on the rope which is attached to his $2.5$-kg sled. The rope makes an angle of $22\degree$ with the nearly friction-less surface. Use the structure provided below to determine the net force on and acceleration of the sled.
> [!NOTE] Question 4
> The custodians clean the field house gym floor between games at the annual Holiday Basketball Classic. Chuck exerts a force on a $1.1$ kg push broom as he walks across the floor at a constant speed. The coefficient of friction between the floor and the broom is $0.45$ and the broom handle makes an angle of $41\degree$ with the horizontal. Determine the amount of force with which Chuck pushes downward (along the handle of the broom) in order to achieve this constant speed motion.
> [!NOTE] Question 5
> Shriyans went rock climbing this past weekend. During one climb through a narrow vertical chimney, he supported his weight by leaning with his back against one wall of the chimney and pushing off the opposite wall with his legs. His left leg made a $26\degree$ angle with the horizontal. The coefficient of friction between his back and the chimney wall is $0.508$. A) Determine the minimum amount of tension which would be required to support the weight of his $86$ kg body (190 pounds). B) Determine the normal force exerted on his by the wall as a result of your answer to part A.
> [!NOTE] Question 6 (Part 1)
> In rage and a hurry to get to his Economics class, Krishna instantaneously slams the crash bar doors leading out of Building 5. In his aggression, he exerts a space-warping $10$ kN (kilo-Newtons) of force on the crash bar. \
> ![](https://upload.wikimedia.org/wikipedia/commons/thumb/1/19/Set_of_Crash_Bar_Doors.jpg/330px-Set_of_Crash_Bar_Doors.jpg) \
> If $\mu_k=0.95$, how quickly does the $1$ kg, $5$ cm deep crash bar transfer all of its momentum into the door (answer in milliseconds)?
> [!NOTE] Question 7 (Part 2)
> If the door weighs $600$ N, what would its linear velocity be directly after impact?
> [!NOTE] Question 8 (Part 3)
> Given that there exists a wall initially on the same plane as the door before the door is set in motion, in how many seconds, $s$, does the door hit the wall if the door is 2 meters wide?
> [!NOTE] Question 9
> How much force is needed to pull a spring with a spring constant of $20$ N/m a distance of $25$ cm?
> [!NOTE] Question 10
> A spring is pulled to $10$ cm and held in place with a force of $500$ N. What is the spring constant of the spring?
> [!NOTE] Question 11
> Suppose a 60.0-kg woman floats in fresh water with 97.0% of her volume submerged when her lungs are full of air. What is her average density?
> [!NOTE] Question 12
> A solid metal ball is falling in a long liquid column and has attained terminal velocity $= 2 \tfrac{m}{s}$. Find the viscosity of the liquid if the radius of metal ball is $r = 5$ cm and its density $\rho_s = 8050 \frac{\mathrm{kg}}{\mathrm{m^3}}$ (density of liquid $l = 1000 \frac{\mathrm{kg}}{\mathrm{m^3}}$ and $g = 10 \tfrac{\mathrm{m}}{{\mathrm{s}^2}}$)
> [!NOTE] Question 13
> Lakshman ($100$ kg) stands upon a wooden board - weighing $100$ N - which is set upon a 3x3 array of springs with a gap in the center, looking like:
>
> | Column1 | Column2 | Column3 |
> |------------|------------|------------|
> | $\psi$ | $\psi$ | $\psi$ |
> | $\psi$ | `<empty>` | $\psi$ |
> | $\psi$ | $\psi$ | $\psi$ |
>
> If they collectively traveled ,via compression, $10$ cm, what is their average spring constant?