A car accelerates uniformly from rest along a straight road at a = 2.5 m/s² for t = 8 seconds. What distance does the car cover during these 8 seconds?
Mechanics Dynamics Kinematics
Question · Easy
Same battery. Which lets more through?
Short
A body of mass m = 4 kg is pulled horizontally along a flat surface by a force F = 20 N. If the coefficient of kinetic friction between the body and the surface is mu = 0.25 (take g = 10 m/s²), what is the acceleration of the body?
A projectile is launched with an initial velocity v0 = 20 m/s at an angle theta = 30° above the horizontal from ground level. Taking g = 10 m/s² and neglecting air resistance, what is the maximum height H_max reached by the projectile?
Question · Medium
A 0.5 kg ball moving with velocity v1 = 6 m/s collides head-on and elastically with a stationary ball of mass 1.0 kg. What is the velocity of the 1.0 kg ball immediately after the collision?
A spring with stiffness k = 400 N/m is compressed by x = 5 cm (0.05 m). What is the potential energy stored in the compressed spring?
What is the period of small oscillations T of a simple mathematical pendulum of length L = 0.98 m on Earth where g = 9.8 m/s²?
A solid wooden block of volume V = 0.002 m³ and density rho_wood = 700 kg/m³ is completely submerged in water (rho_water = 1000 kg/m³, g = 10 m/s²). What is the buoyant (Archimedes) force acting on the block?
A stone is dropped from the top of a tower and hits the ground after t = 3.0 s. Taking g = 10 m/s² and neglecting air resistance, what is the height of the tower?
A satellite moves in a circular orbit around Earth at a distance where the orbital radius is r. If the orbital speed is v, what is the centripetal acceleration of the satellite?
What constant force F, applied parallel to the surface of the incline, is required to push a m = 50 kg crate up a smooth frictionless incline angled at 30° at a constant velocity (take g = 10 m/s²)?
An ideal gas undergoes an isothermal expansion at temperature T = 300 K, increasing its volume from V1 = 2 L to V2 = 6 L. If the initial pressure was P1 = 300 kPa, what is the final pressure P2?
Molecular Physics Thermodynamics
What is the maximum theoretical efficiency (Carnot efficiency) of a heat engine operating between a hot reservoir at T_hot = 500 K and a cold reservoir at T_cold = 300 K?
How much heat Q is required to raise the temperature of m = 2 kg of water from 20°C to 80°C (specific heat capacity of water c = 4200 J/(kg*K))?
In an isobaric expansion at constant pressure P = 2.0 * 10^5 Pa, an ideal gas expands from V1 = 0.01 m³ to V2 = 0.04 m³. What is the work A done by the gas?
What is the average translational kinetic energy of a molecule of an ideal gas at absolute temperature T = 300 K (Boltzmann constant k_B = 1.38 * 10^-23 J/K)?
Two point charges q1 = +4 muC and q2 = -2 muC are separated by a distance r = 0.3 m in vacuum (Coulomb's constant k = 9.0 * 10^9 N*m²/C²). What is the magnitude of the electrostatic force between them?
Electrodynamics Circuits Magnetism
What is the equivalent capacitance of three capacitors with C1 = 6 muF, C2 = 3 muF, and C3 = 2 muF connected in parallel?
A battery with EMF E = 12 V and internal resistance r = 1.0 Ohm is connected to an external load resistor R = 5.0 Ohms. What is the current I in the circuit and the terminal voltage V across the load?
A proton (charge q = 1.6 * 10^-19 C) enters a uniform magnetic field B = 0.5 T with velocity v = 2.0 * 10^6 m/s perpendicular to the magnetic field lines. What is the magnitude of the Lorentz force acting on the proton?
A circular coil of N = 100 turns experiences a change in magnetic flux from Phi1 = 0.05 Wb to Phi2 = 0.01 Wb over a time interval Delta_t = 0.2 s. What is the magnitude of the induced electromotive force (EMF) in the coil?
A light ray travels from water (refractive index n1 = 4/3) into air (n2 = 1.0). What is the critical angle theta_c for total internal reflection?
Optics Quantum Nuclear Physics
An object is placed at a distance d_o = 30 cm in front of a thin converging lens of focal length f = 20 cm. Where is the real image formed, and what is its linear magnification M?
The work function of a metal surface is W = 2.0 eV. If monochromatic light of photon energy E = 3.5 eV shines on the surface, what is the maximum kinetic energy K_max of the emitted photoelectrons?
A radioactive isotope has a half-life T_1/2 = 8 days. If the initial sample contains N0 = 8.0 * 10^12 undecayed nuclei, how many undecayed nuclei remain after t = 24 days?
In a nuclear alpha-decay reaction, uranium-238 (92_U^238) emits an alpha particle (2_He^4). What is the daughter nucleus produced?
A flywheel rotating with initial angular velocity omega0 = 40 rad/s decelerates uniformly with angular acceleration alpha = -5 rad/s². How many revolutions does the flywheel make before coming to rest?
Question · Hard
What is the escape velocity v_esc from the surface of Earth (radius R = 6.4 * 10^6 m, g = 9.8 m/s²)?
A hydraulic press has pistons with cross-sectional areas A1 = 10 cm² and A2 = 500 cm². If a force F1 = 50 N is applied to the smaller piston, what force F2 is exerted by the larger piston?
A simple harmonic oscillator has mass m = 0.2 kg and spring stiffness k = 80 N/m. What is the cyclic frequency (angular frequency omega) of oscillation?
A train of mass M = 500 tonnes (5.0 * 10^5 kg) moving at v = 20 m/s applies brakes and comes to a stop after traveling s = 400 m. What was the average braking force applied?
An ideal monatomic gas (such as Helium) contains nu = 2.0 moles at temperature T = 300 K. What is the internal energy U of this gas (universal gas constant R = 8.31 J/(mol*K))?
In an adiabatic process (no heat exchange, Q = 0), an ideal gas expands and performs work A = 450 J on its surroundings. What is the change in the internal energy Delta_U of the gas?
What happens to the pressure of a fixed mass of ideal gas if its absolute temperature is tripled (T2 = 3*T1) and its volume is halved (V2 = V1 / 2)?
How much heat is required to melt m = 0.5 kg of ice at 0°C into water at 0°C (latent heat of fusion of ice L_f = 3.34 * 10^5 J/kg)?
What is the root-mean-square speed (v_rms) of oxygen molecules (O2, molar mass M = 0.032 kg/mol) at temperature T = 300 K (R = 8.31 J/(mol*K))?
Two resistors with R1 = 6 Ohms and R2 = 3 Ohms are connected in parallel. What is their equivalent resistance?
An electric heater operating at voltage V = 220 V draws a current I = 5.0 A. How much electrical energy does the heater consume in t = 10 minutes?
What is the electric field strength E at a distance r = 0.2 m from a point charge q = +8.0 nC (+8.0 * 10^-9 C) in vacuum (k = 9.0 * 10^9 N*m²/C²)?
A parallel plate capacitor with plate area A = 0.02 m² and plate separation d = 2.0 mm (0.002 m) is filled with air (dielectric constant epsilon = 1, epsilon_0 = 8.85 * 10^-12 F/m). What is the capacitance C?
A straight wire of length L = 0.5 m carrying a current I = 4.0 A is placed in a uniform magnetic field B = 0.6 T at an angle theta = 30° to the field lines. What is the magnetic force (Ampère force) acting on the wire?
What is the energy W stored in the magnetic field of an inductor with inductance L = 0.5 H carrying a current I = 6.0 A?
What is the wavelength lambda of an electromagnetic radio wave broadcast at frequency f = 100 MHz (100 * 10^6 Hz) in vacuum (speed of light c = 3.0 * 10^8 m/s)?
In an LC oscillation circuit, the inductance is L = 2.0 mH (0.002 H) and capacitance is C = 5.0 muF (5.0 * 10^-6 F). What is the natural oscillation period T of the circuit (Thomson's formula)?
What is the optical power D (in diopters) of a thin diverging lens with focal length f = -25 cm (-0.25 m)?
In Young's double-slit interference experiment, light of wavelength lambda = 600 nm (6.0 * 10^-7 m) illuminates two slits separated by d = 0.2 mm (2.0 * 10^-4 m). The screen is placed at distance L = 1.0 m. What is the fringe width (distance between adjacent bright fringes) Delta_x on the screen?
What is the momentum p of a photon of yellow light with frequency f = 5.0 * 10^14 Hz (Planck's constant h = 6.63 * 10^-34 J*s, c = 3.0 * 10^8 m/s)?
According to Bohr's model of the hydrogen atom, when an electron transitions from energy level n = 3 (E3 = -1.51 eV) to n = 1 (E1 = -13.6 eV), what is the energy of the emitted photon?
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