Practice Test 3 - High School Physics

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

A $70\,\text{kg}$ cyclist crashes into a rigid barrier at $v=8\,\text{m/s}$ . You can add handlebar padding that compresses by up to $80\%$ of its thickness during impact. The design goal is to keep the average impact force below $F_{\max}=2500\,\text{N}$ while using the minimum padding thickness. Constraint: the available space allows at most $6.0\,\text{cm}$ of padding thickness. Using $F\approx \dfrac{\Delta KE}{d}$ with $\Delta KE=\tfrac12 mv^2$ , what minimum padding thickness is required, and is it feasible within the space limit?
A radio hobbyist claims that analog signals are always better than digital signals because analog has "infinite resolution" (continuous values). Which response best compares the trade-off in a practical transmission system?
A sealed glass aquarium contains air at 20°C. A small electric heater warms the air near the bottom to about 35°C. Over several minutes, smoke introduced near the bottom rises while cooler smoke near the top sinks, forming a circulating loop. Which mechanism best explains the movement that transfers thermal energy through the air in the tank?
A microphone produces an analog voltage that varies smoothly with sound pressure. A computer stores the recording as a digital audio file made of discrete binary values (0s and 1s) after conversion. Which statement correctly describes how analog and digital signals represent information?
A team is building a portable solar charger that converts solar radiation $\rightarrow$ electrical energy (photovoltaic). In full sun, the sunlight intensity is $I = 1000\,\text{W/m}^2$ . The solar cells have efficiency $\eta = 18\%$ . The charger must deliver $P_{out} \ge 15\,\text{W}$ to power a small radio system. Assuming the panel is pointed directly at the Sun (no angle loss), what minimum panel area $A$ is required? Use: $P_{out} = A\,I\,\eta$ .
A light bulb uses $E_{in}=800\ \text{J}$ of electrical energy in a short time and emits $E_{out}=40\ \text{J}$ of useful light energy. The rest becomes thermal energy. What is the bulb's efficiency $\eta$ (in %)?
In a 1D collision lab, you will use a sign convention: rightward velocities are positive and leftward velocities are negative. Two carts collide and separate. Which data-analysis step is most important to correctly test momentum conservation using measured velocities?
A car's steering wheel airbag is intended to reduce the average force on a driver's chest. During a crash, the driver's upper body (effective mass 40 kg) moves forward at 10 m/s relative to the car and must be brought to rest by the restraint system. Two restraint designs are compared: - Design A: no airbag (seat belt only), stopping time $\Delta t=0.040\,\text{s}$ , contact area on chest $A=0.020\,\text{m}^2$ - Design B: airbag, stopping time $\Delta t=0.120\,\text{s}$ , contact area on chest $A=0.080\,\text{m}^2$ Use $F_{\text{avg}}=\frac{m\Delta v}{\Delta t}$ and pressure $P=\frac{F}{A}$ . Criteria: $F_{\text{avg}}<5000\,\text{N}$ and average pressure on the chest $P<100\,\text{kPa}$ . Which statement is correct?
A $2\,\text{kg}$ cart (Cart A) moving at $5\,\text{m/s}$ to the right hits a stationary $3\,\text{kg}$ cart (Cart B) in 1D. After the collision, Cart B moves at $3\,\text{m/s}$ to the right. How much kinetic energy is transferred to Cart B as kinetic energy during the collision?
A $50\,\text{N}$ horizontal force pushes a box $10\,\text{m}$ across a floor. The kinetic energy of the box increases by $200\,\text{J}$ over that distance. How much energy is transferred into thermal energy due to friction over the $10\,\text{m}$ ? (Assume no other energy changes.)
A $12\,\text{kg}$ crate is pushed across a horizontal floor at constant velocity. The applied force is $F_{\text{app}}=50\,\text{N}$ to the right (→). The forces on the crate are: weight $F_g$ downward (↓), normal force $F_N$ upward (↑), kinetic friction $F_f$ to the left (←), and the applied force to the right (→). Based on this situation, what is the magnitude of the friction force $F_f$ on the crate?
A student is designing a hand-crank generator that converts mechanical rotation → electrical energy for emergency phone charging. The generator must provide an electrical output of at least $P_{out} = 5.0\,\text{W}$ at $V=5.0\,\text{V}$ for at least 10 minutes. The overall efficiency from mechanical input to electrical output is $\eta=40\%$ . The device must have mass $\le 0.60\,\text{kg}$ and cost $\le$25. What minimum mechanical input power $P_{in}$ must the user supply while cranking to meet the electrical output requirement? Use $\eta = \frac{P_{out}}{P_{in}}$ .
A 4.0 kg pendulum bob is released from rest at a height of 2.5 m above its lowest point (take $PE_g=0$ at the lowest point). Ignoring air resistance, what is the bob's speed at the lowest point? Use $g=10\ \text{m/s}^2$ , $PE_g=mgh$ , and $KE=\tfrac12 mv^2$ .
Two identical metal spheres each have mass $m = 1.0\,\text{kg}$ and net charge $q = +1.0\,\mu\text{C} = 1.0\times 10^{-6}\,\text{C}$ . Their centers are $r = 0.50\,\text{m}$ apart. Using $G = 6.67 \times 10^{-11}$ and $k = 9.0 \times 10^9$ , which statement best describes which force dominates and by approximately what factor (magnitude ratio)?
A student holds one end of a copper rod and one end of a plastic rod against the same hot plate. After 30 seconds, the far end of the copper rod is much warmer than the far end of the plastic rod. The rods are not in moving air and are the same size. Which mechanism is being tested most directly by changing the rod material (hot plate → far end of rod)?
A class is comparing momentum conservation for elastic (magnetic bumpers) vs perfectly inelastic (velcro) collisions using two carts on a low-friction track. Which statement describes what counts as success for the momentum part of the investigation (regardless of collision type)?
A coil is connected to a voltmeter that measures the induced voltage. The student repeats the same motion of pushing a magnet into the coil at the same speed, but changes the coil: Coil X has 100 turns and Coil Y has 300 turns. All other factors (magnet, speed, coil area, resistance) are the same. Which comparison of induced EMF magnitudes is correct, based on $|\varepsilon| = N\left|\Delta\Phi/\Delta t\right|$ ?
A student is building a small wind-turbine generator converting mechanical rotation → electrical energy. For a given magnet and coil geometry, the induced voltage is proportional to $N\omega$ (Faraday's law trend), where $N$ is the number of coil turns and $\omega$ is rotation speed. A prototype with $N=200$ turns produces $6.0\,\text{V}$ at $\omega=300\,\text{rpm}$ . The design target is $12.0\,\text{V}$ at the same rotation speed and magnet strength.

What minimum number of turns $N$ should be used?
A digital link uses two voltage levels to represent bits: 0 at 0 V and 1 at 5 V. The receiver decides 0 if the voltage is below 2.5 V and 1 if above 2.5 V. If noise increases so that the received voltage sometimes crosses the 2.5 V decision level, what will you most likely observe compared with an analog link carrying the same information as a continuously varying voltage?
A book rests motionless on a table. Consider only the contact interaction between the book and the table. Which pair of forces is an action-reaction pair?

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