Practice Test 10 - High School Physics

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

A $0.80\,\text{kg}$ mass is launched vertically upward by a spring (ignore air resistance). The spring constant is $k=300\,\text{N/m}$ and it is compressed $0.40\,\text{m}$ . After the mass leaves the spring, how high above the launch point does it rise? (Use $g=10\,\text{m/s}^2$ .)
A point charge $Q=+4.0\,\mu\text{C}$ is fixed at the origin. Point $P$ is located on the +x-axis at $x=0.30\,\text{m}$ . What is the direction of the electric field $\vec{E}$ at point $P$ due to $Q$ ?
In a DC motor, a current-carrying coil sits in a magnetic field and experiences forces that make it rotate. Which energy transformation best describes what happens during steady operation (ignoring losses)?
A rectangular wire loop is placed in a uniform magnetic field $\vec B$ directed to the right (→). The loop is oriented so that the left vertical side carries current upward (↑) and the right vertical side carries current downward (↓). What best describes the forces on the two vertical sides due to the magnetic field?
A rectangular coil rotates at constant speed between the poles of a magnet (a simple generator). The magnetic field in the gap is approximately uniform. As the coil rotates, which change is directly responsible for producing an alternating induced EMF in the coil?
A car bumper insert is being chosen for a low-speed crash (parking collision). The design goal is to maximize energy absorption (reduce rebound) while keeping repair costs low, and it only needs to work once in a severe impact. Which material behavior is most appropriate for reducing forces on occupants by dissipating kinetic energy rather than returning it? Which choice best matches the physics goal?
A student is designing a hand-crank generator that converts mechanical rotation $\rightarrow$ electrical energy (electromagnetic induction) to charge a USB power bank during a camping trip. The device must provide an electrical output power $P_{out} \ge 5.0\ \text{W}$ at $5.0\ \text{V}$ for at least 10 minutes. The generator is expected to be $\eta = 70\%$ efficient (electrical output divided by mechanical input). What minimum mechanical input power $P_{in}$ (from cranking) is required to meet the electrical power requirement? Use: $\eta = \dfrac{P_{out}}{P_{in}}$ .
A 2.0 kg pendulum bob is released from rest at a point $5.0\,\text{m}$ above its lowest point (ignore air resistance, $g=10\,\text{m/s}^2$ ). What is the bob's speed at the lowest point?
For this experiment comparing elastic vs perfectly inelastic collisions, you will use two dynamics carts on a low-friction track. You can swap magnetic bumpers (elastic) and velcro bumpers (perfectly inelastic). Which set of measurements is essential to verify $p_{before}=p_{after}$ for each collision type?
A head-on elastic collision occurs between two carts on a low-friction track. Cart A has mass $m_A = 1.0\ \text{kg}$ with initial velocity $v_{A i} = +4.0\ \text{m/s}$ (right). Cart B has mass $m_B = 1.0\ \text{kg}$ with initial velocity $v_{B i} = -2.0\ \text{m/s}$ (left). After the collision, Cart B is observed moving right at $v_{B f} = +4.0\ \text{m/s}$ . Using conservation of momentum only, what must Cart A's final velocity $v_{A f}$ be (in m/s) for momentum to be conserved?
On a low-friction track (rightward positive), Cart A has mass $m_A = 4.0\,\text{kg}$ and is initially at rest ( $v_{A i} = 0$ ). Cart B has mass $m_B = 1.0\,\text{kg}$ and moves right at $v_{B i} = +12\,\text{m/s}$ . They collide and stick together (perfectly inelastic). What is the common final velocity $v_f$ ?
Two sound waves travel through the same room air (so their speed is the same, $v \approx 343\ \text{m/s}$ ). Wave 1 has frequency $f_1 = 250\ \text{Hz}$ and Wave 2 has frequency $f_2 = 1000\ \text{Hz}$ . How does the wavelength of Wave 1 compare to the wavelength of Wave 2?
A single rectangular loop is rotated at constant speed between the poles of a strong magnet, so the angle $\theta$ between the magnetic field and the loop's area normal changes with time. The loop is connected to a load, forming a closed circuit. Which statement correctly explains why an alternating voltage is produced?
In the Earth–Moon system, the mass of Earth is $M_E = 6.0 \times 10^{24}\ \text{kg}$ and the mass of the Moon is $M_{\text{Moon}} = 7.3 \times 10^{22}\ \text{kg}$ . The distance between their centers is $r = 3.8 \times 10^{8}\ \text{m}$ . Using Newton's Law of Universal Gravitation, $F = G\dfrac{m_1 m_2}{r^2}$ with $G = 6.67 \times 10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2$ , what is the magnitude of the gravitational force between Earth and the Moon?
A battery charging system receives $E_{in}=4000\ \text{J}$ of electrical energy. Measurements show $E_{lost}=600\ \text{J}$ is dissipated as heat. How much useful chemical energy is stored in the battery, $E_{out}$ ? Use: $E_{in}=E_{out}+E_{lost}$
Two masses are connected by a light rope over a frictionless pulley. Mass A ( $m_A=4.0\,\text{kg}$ ) falls $2.0\,\text{m}$ while mass B ( $m_B=2.0\,\text{kg}$ ) rises $2.0\,\text{m}$ . The system starts from rest and, after moving $2.0\,\text{m}$ , both masses have speed $v=3.0\,\text{m/s}$ . Take $g=9.8\,\text{m/s}^2$ . How much energy is converted to thermal energy (e.g., due to axle friction/air resistance) during this motion?
A $4\,\text{kg}$ cart on a horizontal track experiences an applied force $F_{app}=25\,\text{N}$ to the right and a friction force $F_f=5\,\text{N}$ to the left. Using $g=10\,\text{m/s}^2$ , what is the cart's acceleration (magnitude and direction)?
A car at $v=25\ \text{m/s}$ must stop with an average deceleration magnitude less than $a_{\max}=30\ \text{m/s}^2$ to reduce injury risk. Assume constant deceleration and use $v^2=2ad$ to estimate the minimum stopping distance required. Front-end designs (maximum controlled deformation distance available): - Design A: $d=8\ \text{m}$ (too long for the vehicle), cost $$1200. - Design B: $d=12\ \text{m}$ (impossible for the vehicle), cost $$1600. - Design C: $d=10.5\ \text{m}$ (fits exactly), cost $$1500. - Design D: $d=6\ \text{m}$ (fits), cost $$900. Vehicle constraint: $d\le 10.5\ \text{m}$ . Which design meets both the deceleration limit and the vehicle constraint?
A bicycle helmet is being redesigned to reduce concussion risk. In a fall, a rider's head (modeled as 5.0 kg effective mass) hits the ground at 6.0 m/s and comes to rest. Without a helmet, the collision time is about 0.010 s; with a helmet liner that compresses, the collision time can be increased to 0.060 s. Using the impulse-momentum theorem $J = \Delta p = F_{\text{avg}}\Delta t$ , which statement best explains why the compressible liner improves safety?
An electric motor has efficiency $\eta=80\%$ and delivers useful mechanical power $P_{out}=320\ \text{W}$ . What electrical input power $P_{in}$ is required? (Use $\eta=(P_{out}/P_{in})\times 100\%$ .)

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