Work and Energy
SI units & Physics constants
Work and energy investigates different forms of energy, their transmutation, and interrelationship between energy and work
Here (all units see here):
m is mass of object
is force vector
is displacement vector
is angle between vectors and
is velocity
General formulas
Work done by constant force during small displacement is defined by scalar product
Work done by force during motion between initial and final positions is defined by definite integral over trajectory
Instantaneous power is defined as derivative with respect to time
Average power required to perform work W during time t
Relation between power, force and velocity
Kinetic energy of object
Conservative force is the force when the work it does on object is independent of the path between the object's initial and final positions. Otherwise the force is called nonconservative
Potential energy, E_{p}, for conservative force is defined by relation
where:
W is work done by the force
E_{pi} and E_{pf} are potential energies at initial and final positions respectively
Gravitational potential energy of object at height h
where g is freefall acceleration
Total mechanical energy
WorkEnergy Theorem
General WorkEnergy theorem
where:
W is net work done by external nonconservative forces acting on the system
E_{ki}, E _{pi} are initial kinetic and potential energies respectively
E_{kf}, E _{pf} are final kinetic and potential energies respectively
Principal of conservation of energy for conservative system (without nonconservative forces)
Work and energy of spring
Work done by spring
where:
k is spring constant
x_{o} is length of unstretched spring
x_{i} and x_{f} are initial and final lengths of the spring respectively
Potential energy of spring stretched to length x
Energy conservation principal for springmass system
where v_{i} and v_{f} are initial and final speeds of the mass respectively
Work and energy of rotational motion
Work done by torque
where:
is component of net torque parallel to axis of rotation
and are initial and final angular positions of object
Kinetic energy of rotating object
where:
I is moment of inertia of object about its axis of rotation
is angular speed
Total kinetic energy of moving object
where:
v_{c} is linear speed of mass center of the object
is angular speed of the object
m is mass of the object
I_{c} is moment of inertia of the object about the axis of rotation passing through its center of mass
