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Step-by-Step Physics

Wolfram|Alpha helps you explore step-by-step answers to a wide range of physics problems to help with homework or general education. Use flexible formulas to solve different variables for the same equation with topics covering the full range of physics, including electromagnetism, relativity and Newtonian mechanics. Make use of automatic unit conversions by selecting your preferred unit.

Mechanics

Get help solving problems involving the motion of objects under external forces.

Compute average velocity, displacement or time step by step using a single formula:

average velocity, 2 miles over 20 minutes
distance with an average velocity of 60mph in 90 seconds
120 miles at an average velocity of 60mph

Derive the solution for projectile motion:

projectile v=10 meters/second, angle = 30°

Calculate the density of an object step by step:

density for 2kg in 20 L

Derive the solution for the distance covered by a bouncing ball and the restitution coefficient:

bouncing ball after maximum height 12 cm, an initial height of 1 m and 3 bounces

Electricity & Magnetism

Follow the steps for solving equations involving the electromagnetic force.

Derive the force and potential between two electric charges:

coulomb's law for 0.1 C and 0.2 C at 2 meters distance

Compute the steps for the total resistance of resistors in parallel:

2 ohm and 6 ohm resistors in parallel

Explore the computation for capacitance between two concentric spheres:

capacitance between two concentric spheres with radii of 2m and 3m

Calculate the magnetic field inside an ideal solenoid:

magnetic induction of an ideal solenoid with n=20 per meter and current of 2 A

Show the steps for the voltage gain and output voltage of an inverting amplifier:

inverting amplifier with resistance 2 ohms and 20 ohms and an input voltage of 3 V

Relativity

Find the steps for relativistic calculations like time dilation, red shifts and kinetic energy.

Find the steps for relativistic effects like length contraction:

length contraction for a proper length of 1 yard at 0.93c
speed for time dilation for stationary time of 20 minutes to 1 hour

Solve for relativistic red shifts:

relativistic red shift at 0.96c

Compute the steps for relativistic momentum:

relativistic momentum 170 kg at 0.97c

Fluid Mechanics

Solve calculations for the mechanics of fluids step by step.

Calculate flow through a pipe using Poiseuille's law:

water flow through a pipe 2" diameter, 10' length of pipe with 2 kPa pressure difference

Solve for a Reynolds number step by step:

reynolds number in air at 20 mph, 4"

Compute the height reached by capillary action:

capillary action of water for a radius of 0.25 cm at 45 degrees

Oscillations & Waves

Explore the steps for solving common calculations involving waves and oscillating systems.

Find the step-by-step solution for the change in the frequency of sound from a moving source:

Doppler shift for sound at source frequency 100 kHz for 70 mph

Explore the steps to solve for the frequency of a spring under damped harmonic motion:

damped harmonic oscillator, zeta=0.25, spring constant of 12 N/m, mass=2 kg

Calculate the speed of a wave along a string:

wave propagation along a string for a tension of 10 N and linear density of 200 g/m

Thermodynamics

Follow the steps for solving equations for thermodynamic systems and principles.

Compute the change in internal energy:

first law of thermodynamics Q=-1150 J, W=-480 J

Show how to derive the heat capacity ratio:

heat capacity ratio Cp=72.9 J/K, Cv=64.5 J/K

Find the efficiency of thermodynamic cycles step by step:

Bell Coleman cycle, high pressure of 0.6 MPa, low pressure of 0.2 MPa, heat capacity ratio of 1.3
Otto cycle compression ratio of 8, heat capacity ratio of 1.2

Astrophysics

Get step-by-step assistance with astronomy problems.

Convert parallax to distance in parsecs or light years:

parallax distance for 0.3 arcseconds

Compute the steps to determine the period for a body to orbit the sun:

Kepler's third law, 30 AU

Derive luminosity from apparent magnitude and distance:

luminosity apparent magnitude of 4, d=13 light years

Learn the steps to calculate the entropy of a massive black hole:

entropy of a black hole with 200 solar masses

Conservation of Energy

Apply the law of conservation of energy to derive physical properties of a system.

Find the maximum height reached by a projectile launched from the ground:

projectile maximum height with initial speed 30 m/s, gravitational acceleration 2 g

Determine the maximum velocity reached by a pendulum:

small oscillation pendulum max velocity 2 m, 5 degrees

RELATED EXAMPLES

  • Electricity & Magnetism
  • Fluid Mechanics
  • Mechanics
  • Optics
  • Oscillations & Waves
  • Physics
  • Quantum Physics
  • Relativity
  • Thermodynamics

    • Optics

    Compute the steps for solving optics equations, including refraction, reflection and diffraction.

    Find the steps to solve for the angle of refraction:

    Snell's law for air and water, angle of incidence of 10 degrees

    Solve for image distance and magnification in different mirrors:

    concave mirror with a focal length of 3 meters and an object at 5 meters
    convex mirror with a focal length of 3 meters and an object at 5 meters

    Explore lens equations step by step:

    thin lens equation, object distance of 3 feet and image distance of 2 feet
    two lens in contact, focal length 1 of 10 cm and focal length 2 of 5cm, and object distance of 20 cm

    Quantum Mechanics

    Compute the steps for solving calculations involving quantum mechanics.

    Solve for the energy of a photon given its wavelength:

    photon energy 435nm

    Find the steps to solve for the Compton wavelength shift:

    Compton scattering of electron at 30 degrees

    Compute the broadening of emitted wavelengths due to quantum uncertainty:

    natural broadening at 456.8 THz and 100 ns

    Apply the de Broglie relationship to find the wavelength of particles moving at high speed:

    de Broglie relations for a neutron at 10 MeV
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