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