Work, energy and power Flashcards
Work (mathematical relationships)
F Δx cosϴ, Where: -F is the magnitude of the force -Δx is the magnitude of displacement -ϴ is the angle between the force and the displacement
Positive net/total work
Energy is transferred to the object in the direction of original displacement
increase an object’s kinetic energy
What happens when work is done on a system?
What is the effect of work done on abject by a force?
work done = energy transferred
- Energy is transferred from one object to another object (energy is transfers within a system)
- The amount of work done by a force is equal to the energy transfer taking place
When is positive work done on an object?
When ϴ is less than 90°
cos 0 = 1
cos 90 = 0
this will mean that the force (or at least a component if it ) acts in the direction of the initial displacement of the object
Zero work
Done on object by a force that acts at 90° to the direction of object’s displacement
Energy of object remains unchanged
When do we get negative work
When ϴ is more than 90°
cos 180 = - 1
Negative
Done by a force which acts against the motion of the object
Energy is removed from the system/object and transferred to other forms of energy
Work (explained in words)
Work is done when a force acts on an object and it moves in the direction of the force.
Work done is equivalent to the energy transferred
Net work (mathematical relationships) 2 methods
Calculated by adding positive and negative work done by each force
- W net = Σ W of individual forces
(We add the work done by each force algebraically since work is a scalar quantity)
OR - W net = F net Δx cosϴ
Work unit analysis
Joules
(Recall: Work done is equivalent to the energy transferred)
Work is a scalar quantity as energy does not have direction
Gravitational potential energy
Energy of an object due to its position in a gravitational field relative to a reference point
(reference point is usually the surface of the earth)
Potential energy (unit analsis)
The energy possessed by an object because of its position relative to other objects
Ep = mgh
units: Joules
Kinetic energy
Energy of an object because of its motion
Ek = 1/2 mv^2
units: joules
Mechanical energy
Em = Ep + Ek Em = mgh + 1/2 mv^2
The sum of (gravitational) potential energy and kinetic energy
Law/principle of the conservation of mechanical energy
Σ Em initial = Σ Em final
Eki + Epi = Ekf + Epf
Total mechanical energy, as the sum of Ep and Ek, in an isolated system remains constant
(no non-conservative forces present > only gravitational potential force allowed to be included in system as it is a conservative force)
Work-energy theorem (mathematically)
Wnet = ΔEk Wnet = Ekf - Eki
Work-energy theorem (in words)
Wnet = ΔEk
The net/total work done on an object is equal to the change in the object’s kinetic energy
The work done on an object by a resultant/net force is equal to the the change in the object’s kinetic energy
Net positive and negative work done describes in terms of the work energy system
The net positive work done on an object will be equal to the increase in the kinetic energy of the object
The net negative work done on an object will be equal to the decrease in kinetic energy of the object
isolated system
NB: A system in which the resultant/net external force acting on the system is zero
In terms of conservation of Em, no non-conservative forces present
Conservative force
NB: A force for which the work done in moving an object between two points is independent of the path taken.
Wnet of conservative force = 0, while moving an object around a closed path (start and end at same point)
Examples of conservative forces
Gravitational force
Elastic force in a spring
Electrostatic forces (coulomb forces)
Non-conservative force
Given by symbol: Wnc
NB: A force for which the work done in moving an object between two points depends on the path taken
The net work done by a non-conservative force as an object moves thorough a closed path is NOT zero.
Non-conservative forces transfer Em of object to surroundings. Em is not conserved.
Examples of non-conservative forces
Frictional force
Air resistance
Tension in a chord
^^^tension: Applied forces (positive or negative work is always done thus Em not conserved)
Discuss why mechanical energy is not conserved by non-conservative forces
Non-conservative forces are dissapative forces.
Dissapative forces convert mechanical energy into other forms of energy (most commonly thermal energy)
2ed form of the work energy theorem (mathamatically)
Wnc = ΔEk + ΔEp
2ed form of the work energy theorem (in words)
The work done by all non-conservative forces equals the change in the total mechanical energy of the system
Fgx or Fg // component of gravity
mgsinϴ
Fgy or Fg perp component of gravity
mgcosϴ
Define power in words and mathematically in an equation
Power is the rate at which work is done
or the rate at which energy is expanded
P = W/Δt
1 kW = ..
1 000 W
1 Watt is what is terms of other SI units
1 J. s -1
Power time relationship
Inversely proportional.
P = W/t
What does it mean if A has a greater power output than B?
A has the ability to convert STORED energy within the body INTO MECHANICAL energy
at a GREATER rate than B
Give an equation for average power
state it in words
Pavg = F x Vavg
The average power required to keep an object moving at constant speed is found by multiplying the applied force by the average speed of the object
When working with electric motors problems (borehole) what is it important to remember
The electric motor pumps water at a constant rate
This means that the water will move through pipe at constant speed
If there is no change in speed of water than ΔEk = 0
Law of conservation of energy
Energy cannot be created or destroyed. It can only be transferred from one body to another
