Physics: Work and Energy

Work

  • work is the energy transferred when a force acts on an object to cause displacement

  • if force is constant, work can be calculated by using:

    • W = |F||d|cosθ

  • if force and displacement are in the same direction, the angle θ between them is 0, and since cos(0) = 1, the formula is simplified to:

    • W = Fd

  • when force and displacement align, all the force contributes to work

  • if force and displacement are perpendicular, no work is done

  • work is measured in Joules (J)

Conservative Forces

  • the work done by a conservative force is independent of the path taken and relies only on the initial and final positions

  • the total work done by a conservative force along a closed path is always zero

  • nonconservative forces rely on the route taken to displace an object between two different points

    • ex: friction, air resistance

Energy

  • kinetic energy depends on two things:

    • mass - heavier objects have more kinetic energy

    • velocity - the faster something moves, the more kinetic energy it has.

  • KE = ½mv²

  • work-kinetic energy theorem: the net work done on an object equals the change in its kinetic energy

  • when a force acts on an object and causes it to move, the work done by the force changes the object’s KE

    • Wnet = KE = KEfinal - KEinitial

  • potential energy is the energy an object has because of its position, condition or configuration

  • conservative forces are always associated with potential energy

  • spring or elastic force: compressing or stretching a spring stores energy, which is no longer available when the spring returns to its initial state

  • electrostatic force: potential energy is stored in charged particles due to the electrostatic interaction between two charges and how far apart they may be.

  • work done by a conservative force:

    • W = -ΔU

  • work is negative if you are working against the force

  • gravitational potential energy:

    • PE = mgh

  • Hooke’s law:

    • F = -kx

  • power: the rate at which work is done; how quickly you transfer or use energy

    • P = W/Δt