= (2 kg) (9.81 m/s 2 ) (20 m)
= 392 (J, Nm)
The work made by a person of 150 lb climbing a stair of 100 ft can be calculated as
W F = (150 lb) (100 ft)
= 15000 ft lb
The force exerted by springs varies with the extension or compression of the spring and can be expressed with Hooke's Law as
F spring = - k s (3)
F spring = spring force (N, lb f )
k = spring constant
The work done by a spring force is visualized in the chart above. The force is zero with no extension or compression and the work is the half the product force x distance and represented by the area as indicated. The work done when a spring is compressed or stretched can be expressed as
W spring = 1/2 F spring_max s
= 1/2 k s 2 (4)
W spring < = work done (J, ft lb f )
F spring_max = maximum spring force (N, lb f )
A spring is extended 1 m . The spring force is variable - from 0 N to 1 N as indicated in the figure above - and the work done can be calculated as
W spring = 1/2 (1 N/m) (1 m) 2
= 0.5 (J, Nm)
The spring constant can be calculated by modifying eq. 4 to
k = 2 (0.5 J)/ (1 m) 2
= 1 N/m
Rotational work can be calculated as
W M = T θ (5)
W M = rotational work done (J, ft lb)
T = torque or moment (Nm, ft lb)
θ = displacement angle ( radians )
A machine shaft acts with moment 300 Nm . The work done per revolution (2 π radians ) can be calculated as
W M = (300 Nm) ( 2 π )
= 1884 J
Force can be exerted by weight or pressure:
W = ∫ F ds
= ∫ m a g dh
=∫ p A ds
=∫ p dV (6)
W = work (J, Nm)
F = force (N)
ds = distance moved for acting force, or acting pressure (m)
m = mass (kg)
a g = acceleration of gravity (m/s 2 )
dh = elevation for acting gravity (m)
p = pressure on a surface A, or in a volume (Pa, N/m 2 )
A = surface for acting pressure (m 2 )
dV = change in volume for acting pressure p (m 3 )
Power is the ratio of work done to used time - or work done per unit time.
Motion - velocity and acceleration, forces and torque.
Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
Work, heat and energy systems.
The First Law of Thermodynamics simply states that energy can be neither created nor destroyed (conservation of energy). Thus power generation processes and energy sources actually involve conversion of energy from one form to another, rather than creation of energy from nothing.
Required forces to move bodies up inclined planes.
Energy is the capacity to do work.
Newton's third law - force vs. mass and acceleration.
Heat vs. work vs. energy.
Impact forces acting on falling objects hitting the ground, cars crashing and similar cases.
Elevation and potential energy in hydropower.
Power is the rate at which work is done or energy converted.
Calculate pumps hydraulic and shaft power.
Calculate steps, unit rise and run in a staircase.
The work done and power transmitted by a constant torque.
Calculate specific work done by pumps, fans, compressors or turbines.
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