Practice Test 2 - High School Physics

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

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1. A car safety team is designing an airbag system. In a 40 km/h (11.1 m/s) frontal crash, a 70 kg occupant must be brought to rest by the restraint system. To reduce injury risk, the design criterion is to keep the average force on the occupant below 5000 N. Assuming the occupant's momentum changes from $mv$ to 0, what minimum stopping time $\Delta t$ must the airbag + seat belt system provide (treating the force as approximately constant)? Use $F_{avg} = \Delta p/\Delta t$.
2. A 60 kg test dummy moves at $v=12\ \text{m/s}$ before hitting a padded wall and stopping. Designers can tune the padding to increase the collision time $\Delta t$. Safety requires the average force to be at most $F_{\max}=1800\ \text{N}$ using $F_{\text{avg}}=\Delta p/\Delta t$. A mechanical constraint limits the maximum achievable collision time to $\Delta t\le 0.50\ \text{s}$. What is the minimum collision time required, and is it achievable?
3. A $25\,\text{kg}$ cart moving at $8.0\,\text{m/s}$ is brought to $2.0\,\text{m/s}$ by a constant friction force over a distance of $10\,\text{m}$ on level ground. What is the magnitude of the friction force? (Take friction as the only horizontal force doing work.)
4. Two systems transmit the same spoken message: System 1 sends the voice as an analog waveform; System 2 sends it as a digital bitstream (0s and 1s). If interference increases gradually, which prediction best matches typical behavior of the received signal quality?
5. A battery pack converts chemical → electrical energy to power a drone. The drone requires $P=120\,\text{W}$ continuously for $t=15\,\text{min}$. Assume the battery can deliver the required power and ignore losses.
   
   What minimum stored energy must the battery supply (in Joules)?
6. Two students, Student A and Student B, play tug-of-war using a rope. Student A pulls the rope to the left (←) while Student B pulls to the right (→). Focusing on the Student A–rope interaction, which pair of forces is an action-reaction pair?
7. A laboratory measures the energy transported by waves on a string and finds the relationship can be modeled by $E = kA^2$ (with $k$ constant for the setup). If the amplitude decreases from $A_1$ to $0.5A_1$, by what factor does the energy change (ratio $E_2/E_1$)?
8. A student uses a fan to blow air across a warm laptop surface at 45°C in a 22°C room. The laptop cools faster with the fan on than with the fan off. What change best explains the faster cooling?
9. Two parallel metal plates create a uniform electric field between them. A small positively charged bead is released from rest and accelerates toward the negative plate without touching anything else. Which statement correctly identifies the mechanism and energy source for the bead's kinetic energy gain?
10. A proton and an electron are separated by some distance $r$. If the distance is doubled to $2r$, how do the magnitudes of the gravitational force and the electric force between them change?
11. A heat engine produces useful work energy $E_{out}=2400\,\text{J}$ from a thermal energy input $E_{in}=8000\,\text{J}$. How much energy is lost as waste heat, $E_{lost}$?
12. A small satellite orbits Earth. Ignoring all other objects, which pair of forces is the Newton's Third Law action-reaction pair for their gravitational interaction?
13. A $70\ \text{kg}$ student stands on Earth's surface. Take Earth's mass as $M_E = 6.0 \times 10^{24}\ \text{kg}$ and Earth's radius as $R_E = 6.4 \times 10^{6}\ \text{m}$. Using $F = G\dfrac{M_E m}{R_E^2}$ with $G = 6.67 \times 10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2$, what is the magnitude of the gravitational force (weight) on the student?
14. Two charges exert an electric force of $F = 18\,\text{N}$ on each other when separated by $r = 0.30\,\text{m}$. If the charges are unchanged, what will the force be when the separation is reduced to $0.10\,\text{m}$? (Use the inverse-square relationship.)
15. In a simple DC motor, a current-carrying loop experiences a magnetic force due to an external magnetic field, causing the rotor to turn and lift a small mass. Which energy-transfer description is most accurate for how the rotor gains mechanical energy without direct contact with the magnet?
16. A 1.0 kg cart moving at 6.0 m/s collides with a 2.0 kg cart initially at rest on a level track. After the collision, the carts stick together and move at 2.0 m/s. During this interaction, which statement best describes what happens to the "missing" kinetic energy?
17. A building installs a security camera feed over a 300 m cable that runs near a motor causing intermittent electromagnetic interference. The system can use analog video or digital video with error correction. During motor start-up, brief bursts of interference occur. Which observation best matches typical behavior?
18. A helmet designer must keep an athlete's peak head acceleration below 100 g during a fall where the head's impact speed is 6.0 m/s and the effective head mass is 5.0 kg. Approximate the average impact force using work-energy: the padding must absorb the kinetic energy $\tfrac12 mv^2$ over compression distance $d$, so $F_{\text{avg}}\approx \text{KE}/d$ and $a\approx F_{\text{avg}}/m$. Design A: soft foam, thickness/compression distance $d=0.010\,\text{m}$ Design B: multi-density foam, $d=0.030\,\text{m}$ Design C: air-pocket liner, $d=0.050\,\text{m}$ Which design best meets the 100 g requirement (take $g\approx 9.8\,\text{m/s}^2$)?
19. Earth and the Sun are separated by about $r = 1.5 \times 10^{11}\ \text{m}$ (center to center). Use $M_E = 6.0 \times 10^{24}\ \text{kg}$, $M_{\text{Sun}} = 2.0 \times 10^{30}\ \text{kg}$, and $G = 6.67 \times 10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2$. What is the magnitude of the gravitational force between Earth and the Sun?
20. Students use two dynamics carts and motion sensors to test $p_{\text{before}} = p_{\text{after}}$ for a 1D collision. They notice their percent differences vary from 2% to 12% across trials. Which change would most directly reduce uncertainty and improve reliability of the momentum comparison?

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