Practice Test 7 - High School Physics

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. Two spheres are separated by $r = 0.20\ \text{m}$. Sphere A: $m_A = 5.0\ \text{kg}$, $q_A = +1.0\ \mu\text{C}$. Sphere B: $m_B = 5.0\ \text{kg}$, $q_B = +1.0\ \mu\text{C}$. Calculate the magnitudes of both forces, $F_{\text{grav}}$ and $F_{\text{elec}}$.
2. An oscilloscope displays two signals: Signal X is a smooth waveform that varies continuously with time; Signal Y switches abruptly between two voltage levels labeled "low" and "high," corresponding to 0 and 1. Which identification is correct?
3. A $2.0\,\text{kg}$ ball is released from rest from a balcony $5.0\,\text{m}$ above the ground (take $g = 10\,\text{m/s}^2$ and define the ground as $h=0$). Ignoring air resistance, which equation correctly applies conservation of energy from the release point to just before the ball hits the ground?​
4. A proton and an electron are separated by $r = 1.0 \times 10^{-10}\,\text{m}$. Use $m_p = 1.67 \times 10^{-27}\,\text{kg}$, $m_e = 9.11 \times 10^{-31}\,\text{kg}$, $q_p = +1.6 \times 10^{-19}\,\text{C}$, $q_e = -1.6 \times 10^{-19}\,\text{C}$, $G = 6.67 \times 10^{-11}$, and $k = 9.0 \times 10^9$. Which option is closest to the magnitudes of $F_{\text{grav}}$ and $F_{\text{elec}}$? (Compute each force magnitude using the formulas.)
5. An electric motor has efficiency $\eta=90\%$ and takes in $P_{in}=300\ \text{W}$ of electrical power. What is the useful mechanical output power $P_{out}$? Use: $\eta=\left(\frac{P_{out}}{P_{in}}\right)\times 100\%$
6. A phone company compares an older analog voice link (voice waveform sent directly) with a modern digital voice link (voice converted to binary 0s and 1s and transmitted). The company wants calls to stay clear over long distances with repeaters along the way. Why is the digital system typically preferred?
7. A 1200 kg car hits a rigid barrier at $v=15\ \text{m/s}$. The front-end crumple zone length $d$ can be designed to reduce average impact force, modeled by $F\approx \text{KE}/d$, where $\text{KE}=\tfrac12 mv^2$. Safety requires $F\le 2.0\times 10^5\ \text{N}$. However, styling constraints limit the crumple distance to $d\le 0.80\ \text{m}$. What is the minimum crumple distance $d_{\min}$ needed, and is it within the design limit?
8. A $1.0 \times 10^{3}\ \text{kg}$ spacecraft is $r = 1.0 \times 10^{7}\ \text{m}$ from the center of Earth. Use $M_E = 6.0 \times 10^{24}\ \text{kg}$ and $G = 6.67 \times 10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2$. What is the magnitude of the gravitational force Earth exerts on the spacecraft (and, by Newton's Third Law, the magnitude the spacecraft exerts on Earth)?
9. An audio message is sent through a noisy relay system 5 times (each relay receives and forwards the signal). In the analog method, each relay amplifies the waveform (and any noise on it). In the digital method, each relay re-times and regenerates the 0/1 pulses and uses error detection to flag corrupted packets. What will you most likely hear after 5 relays if the noise level is moderate (below the digital failure threshold)?
10. A 1200 kg car traveling at 18 m/s crashes head-on and is brought to rest by its crumple zone length $d$. The design goal is to minimize the average force on occupants, with a safety limit of $F_{\max}=90{,}000\ \text{N}$. The vehicle design allows at most $0.80\ \text{m}$ of front-end deformation. Assuming constant average force, what is the minimum crumple distance needed to keep $F\le F_{\max}$, and does it fit within the $0.80\ \text{m}$ limit? Use $F=\text{KE}/d$.
11. Two people make a 200 km phone call. They can use (1) an analog phone line with periodic amplifiers, or (2) digital VoIP sent over a digital link with repeaters that detect 0/1 and regenerate the pulses. Noise and attenuation increase with distance, and amplifiers boost both signal and noise. Which statement best compares long-distance performance?
12. A heat engine takes in thermal power $P_{in}=900\,\text{W}$ from burning fuel and produces useful mechanical power $P_{out}=270\,\text{W}$. The rest is waste heat to the surroundings. What is the engine's efficiency (as a percentage)?
13. An audio program is distributed to three radio stations by repeatedly relaying the signal through intermediate links. Option 1: send it as an analog audio waveform. Option 2: send it as digital audio with error detection and occasional retransmission when packets fail checksums. Over many relays, which comparison is most accurate?
14. A 0.10 m segment of straight wire is placed between the poles of a horseshoe magnet where the magnetic field is uniform and points into the page (⊗), $B=0.20\,\text{T}$. The wire carries current upward (↑), $I=3.0\,\text{A}$. In which direction is the magnetic force on the wire segment?
15. Two sound waves in air travel at the same speed $v = 343\ \text{m/s}$. Wave 1 has frequency $f_1 = 500\ \text{Hz}$ and Wave 2 has frequency $f_2 = 2000\ \text{Hz}$. Which statement correctly compares their wavelengths?
16. A 3.0 kg sled starts from rest at the top of a hill of height $8\,\text{m}$ and slides down a rough slope. At the bottom, its speed is measured to be $10\,\text{m/s}$ (take $g=10\,\text{m/s}^2$). How much energy was converted to thermal energy by friction during the slide?
17. A transformer has a primary coil connected to an AC source and a secondary coil connected to a lamp. The coils are separated by an insulating core so there is no direct electrical connection between them. Which statement best describes how energy gets from the primary coil to the lamp?
18. A conducting loop is connected to a galvanometer and sits in a uniform magnetic field pointing out of the page. This time, the field strength is steadily decreased (so $B$ decreases with time). According to Lenz's law, what is the direction of the induced current in the loop (viewed facing the page)?
19. Two objects are separated by the same distance $r$. Object 1 has mass $m_1$ and charge $q_1$, and object 2 has mass $m_2$ and charge $q_2$. Which expression correctly gives the ratio of the magnitude of the electric force to the magnitude of the gravitational force between them? Use $F_{\text{grav}} = G\dfrac{m_1m_2}{r^2}$ and $F_{\text{elec}} = k\dfrac{|q_1q_2|}{r^2}$.
20. In designing an investigation to compare collision types, students will run two trials on the same low-friction track: (1) carts with magnetic bumpers (more elastic) and (2) carts with velcro bumpers (perfectly inelastic, carts stick). They will measure $m_1$, $m_2$, $v_{1i}$, $v_{2i}$, $v_{1f}$, and $v_{2f}$. Which data analysis best tests momentum conservation in each trial?

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