MCAT Physics Formulas

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MCAT Physics Formulas
2014-05-03 10:56:51
Physics MCAT Science

All of the formulas for the Physics portion of the MCATs. Formula on one side and name (if applicable) with description of use on the other side.
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  1. Calculating average speed
    • d = distance
    • t = time
  2. Calculating average velocity
    • displacement over time elapsed
  3. Calculate average acceleration
    • change in velocity over elapsed time
  4. Relate change in velocity, acceleration, and time without position.
    1-dimensional, constant acceleration
  5. Relate change in position, initial velocity, acceleration, and time without final velocity. 1-dimensional, constant acceleration
  6. Relate change in velocity, acceleration, and change in position without time. 1-dimensional, constant acceleration
  7. Free fall from 0 velocity

    • g = -9.8m/s^2
    • h = height of fall
  8. For a vector of magnitude v making an angle θ with the x-axis, what are the components in 2-dimensions?

      at an angle
  9. Centripetal acceleration toward the center of a circle with radius r for an object traveling with constant speed v
  10. Newton's first law of motion (Equilibrium)

    Every body continues in its state of rest or of uniform speed as long as no net force and no net torque act on it.
  11. Newton's second law of motion (Dynamics)

    acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. Direction of a corresponds to direction of net F action on the object
  12. Newton's third law of motion

    Whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first.
  13. Instantaneous velocity if position, x, as a function of time, t, is given as:

  14. Relative motion in a moving frame, B.

    • vA is object's velocity in a stationary frame
    • VB is the velocity of the frame
  15. Law of sines
  16. Law of cosines
  17. Projectile Motion: Horizontal Range and flight time if start and end height are equal.
    • (max value) when
  18. Quadratic formula
  19. Projectile motion x and y travel components

    t in x and y equations is the same, no acceleration in the x direction
  20. Momentum
  21. Centripetal force in uniform circular motion
  22. Acceleration in nonuniform circular motion
    • Separate acceleration vector into centripetal and tangential accelerations
    •    and
  23. Relate centripetal acceleration, orbital period, and radius
  24. Hooke's Law of an ideal spring over a limited range of stretch/compression relates Force with distance of stretch given a constant, k.
  25. Motion on an inclined plane (ignoring friction)
  26. Static frictional force
  27. Force of kinetic friction

  28. Drag force moving through a fluid; relating density, area, and speed.

    • C is the experimentally determined drag coefficient, ρ is the fluid density, A is the cross sectional area of the object, v is speed
    • Direction opposite the object's motion relative to the fluid
  29. Pulleys and opposing forces including friction (modified Atwood machine with opposing dangling masses A & C and mass B between them on a frictional surface)

    No friction:
  30. Universal Gravitation - the force of gravity between any 2 objects

    m's are masses; r is the center-center distance
  31. Universal Gravitation in a Circular Orbit

  32. Torque (twisting force)

    • F is force applied
    • l is the length of the lever arm
  33. Work (in Joules, J) done by a constant force of magnitude F on an object as it is displaced by a distance, d at an angle θ to each other.

  34. Work from a varying force (1-dimension or 3-D)

  35. Work from a spring (force varies with distance)
  36. Fundamental Forces
    • Gravitational - attractive force between all matter
    • Electroweak (electromagnetic and weak nuclear) - virtually all of the nongravitational
    • Color force (nuclear strong) - force between quarks, holds protons and neutrons together
  37. Kinetic energy, K, for a mass, m, traveling at a speed, v.
  38. Work-energy theorem: relating work due to nonconservative forces, W_nc and energy

    The sum of the changes in kinetic, potential, and internal energy due to friction
  39. Net Work and Kinetic energy
  40. Conservative forces

    • Gravitational, Elastic spring, & Electric forces
    • Path Independent
  41. Non-conservative Forces
    • Friction
    • Air Resistance
    • Tension
    • Normal Force
    • Propulsion of a motor
    • NOT path independent
  42. Conservation of Mechanical Energy (ignores non-conservative forces)

  43. Potential energy is the negative of the work done by a conservative force (general)
  44. Potential energy with force and path parallel
  45. Potential Energy with a constant force
  46. Gravitational Potential Energy
    • (close to Earth's surface)
    • Generally:
  47. Elastic (spring) potential energy

    Set U=0 @ x=0:
  48. Rest mass energy - the energy inherent to a particle by nature of it having a mass.
  49. Power, P, is the rate at which work is done.  Also described in terms of force, F, and velocity, v and the angle, θ, between them.

    in Joules/sec = Watts
  50. Conservation of linear momentum

    • Total momentum remains unchanged
  51. Impulse

    impulse = change in momentum = product of average force over a time interval
  52. Elastic collisions: bodies do not stick together, internal forces conservative, no sound or heat
    •   and 
  53. Totally Inelastic Collisions: bodies stick together, maximum loss of mechanical energy that supports conservation of momentum
  54. Elastic collisions, special cases relating m1 and m2 and final velocities

    • in 1-D if v2i=0
  55. Center of Mass - average location for the total mass of the system
  56. Density and Specific Gravity

  57. Pressure (generally)
      Force over Area in Pascals (Pa)
  58. Hydrostatic Pressure at a fixed depth, y.
  59. Buoyant Force, upward and equal to the weight of the fluid that the object displaces.

    Density x volume = mass
  60. The continuity equation describes volume flow rate as a function of the cross-sectional area of the pipe and the velocity of the fluid.

  61. Bernoulli's Equation - pressure energy, potential energy, and kinetic energy

    Pressure + Potential (density*gh) + kinetic (velocity) energies in total don't change
  62. Elastic Modulus of a solid (equation)

  63. 3 types of modulus of elasticity
    • Young's modulus (E) for tensile stress (2 equivalent opposing parallel forces in same plane)
    • Shear modulus (G) for shear stress (tensile but not lined up in same plane)
    • Bulk modulus (B) for compression and expansion (forces from all sides)
    • High modulus is rigid (metal and ceramic)
    • Low modulus is elastic (rubber)
  64. Wave velocity
  65. Wave period
  66. Sound Decibels

    a difference of 10dB means intensity differs by a factor of 10 (90dB is 10 times louder than 80dB)
  67. Standing waves - both ends fixed or free
    • n=1, 2, 3, ...
    • L= string or pipe length
    • each end is a node or antinode