Work done by Force
Work done by a force acting on an object.
When a body is moved as a result of a force being applied to it  work is done .
Work done by a Constant Force
The amount of work done by a constant force can be expressed as
W _{ F } = F s (1)
where
W _{ F } = work done (J, ft lb_{f} )
F = constant force acting on object (N, lb_{f} )
s = distance object is moved in direction of force (m, ft)
The unit of work in SI units is joule (J) which is defined as the amount of work done when a force of 1 Newton acts for distance of 1 m in the direction of the force.
 1 J (Joule) = 0.1020 kpm = 2.778x10 ^{ 7 } kWh = 2.389x10^{4} kcal = 0.7376 ft lb_{f} = 1 (kg m^{2})/s^{2}= 1 watt second = 1 Nm = 1 ft lb = 9.478x10^{4} Btu
 1 ft lb_{f} (foot pound force) = 1.3558 J = 0.1383 kp m = 3.766x10 ^{ 7 } kWh = 3.238x10^{4} kcal = 1.285x10^{3} Btu
This is the same unit as energy .
The work done by a constant force is visualized in the chart above. The work is the product force x distance and represented by the area as indicated in the chart.
Example  Constant Force and Work
A constant force of 20 N is acting a distance of 30 m . The work done can be calculated as
W _{ F } = (20 N) (30 m)
= 600 (J, Nm)
Example  Work done when lifting a Brick of mass 2 kg a height of 20 m above ground
The force acting on the brick is the weight and the work can be calculated as
W _{ F } = F s
= m a _{ g } s (2)
= (2 kg) (9.81 m/s^{2}) (20 m)
= 392 (J, Nm)
Example  Work when Climbing Stair  Imperial units
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
Work done by a Spring Force
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)
where
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)
where
W _{ spring < } = work done (J, ft lb_{f} )
F _{ spring_max } = maximum spring force (N, lb_{f} )
Example  Spring Force and Work
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
Work done by Moment and Rotational Displacement
Rotational work can be calculated as
W _{ M } = T θ (5)
where
W _{ M } = rotational work done (J, ft lb)
T = torque or moment (Nm, ft lb)
θ = displacement angle ( radians )
Example  Rotational Work
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
Representations of Work
Force can be exerted by weight or pressure:
W = ∫ F ds
= ∫ m a _{ g } dh
=∫ p A ds
=∫ p dV (6)
where
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 vs. Work
Power is the ratio of work done to used time  or work done per unit time.
Related Topics

Dynamics
Motion of bodies and the action of forces in producing or changing their motion  velocity and acceleration, forces and torque. 
Mechanics
The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more. 
Thermodynamics
Work, heat and energy systems.
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