Chapter 6: Conservation of work, energy, and power.
Work:
• Work is the transfer of energy by a force acting on an object as it is displaced.
• The work W that a force F does on an object is the product of the magnitude F of the force, times the
magnitude d of the displacement, times the cosine of the angle θ between them.
In symbols, W=Fdcosθ.
• The SI unit for work and energy is the joule (J), where 1J=1N⋅m=1 kg⋅m2/s2.
• The work done by a force is zero if the displacement is either zero or perpendicular to the force.
• The work done is positive if the force and displacement have the same direction, and negative if they have
opposite direction
Kinetic Energy and the Work-Energy Theorem
• The net work Wnet is the work done by the net force acting on an object.
• Work done on an object transfers energy to the object.
• The translational kinetic energy of an object of mass m moving at speed v is 𝐾𝐸 =1mv2/2
• The work-energy theorem states that the net work Wnet on a system changes its kinetic energy,
Wnet = 1mv2/2 -1mv2/2
Gravitational Potential Energy
• Work done against gravity in lifting an object becomes potential energy of the object-Earth system.
• The change in gravitational potential energy, ΔPEg, is ΔPEg=mgh, with h being the increase in height
and g the acceleration due to gravity.
• The gravitational potential energy of an object near Earth’s surface is due to its position in the mass-Earth
system. Only differences in gravitational potential energy, ΔPEg, have physical significance.
• As an object descends without friction, its gravitational potential energy changes into kinetic energy
corresponding to increasing speed, so that ΔKE= −ΔPEg.
Conservative Forces and Potential Energy
• A conservative force is one for which work depends only on the starting and ending points of a motion, not
on the path taken.
• We can define potential energy (PE) for any conservative force, just as we defined PEg for the
gravitational force.
• The potential energy of a spring is 𝑃𝐸𝑠 = 1kx2/2, where k is the spring’s force constant and x is the
displacement from its undeformed position.
, • Mechanical energy is defined to be KE+PE for a conservative force.
• When only conservative forces act on and within a system, the total mechanical energy is constant. In
equation form,
KE+PE=constant
or
KEi+PEi=KEf+PEf
where i and f denote initial and final values. This is known as the conservation of mechanical energy.
Power
Power is the rate at which work is done, or in equation form, for the average power P for work W done over
a time t, P=W/t.
The SI unit for power is the watt (W), where 1 W=1 J/s.
The power of many devices such as electric motors is also often expressed in horsepower (hp), where
1hp=746 W.
Work:
• Work is the transfer of energy by a force acting on an object as it is displaced.
• The work W that a force F does on an object is the product of the magnitude F of the force, times the
magnitude d of the displacement, times the cosine of the angle θ between them.
In symbols, W=Fdcosθ.
• The SI unit for work and energy is the joule (J), where 1J=1N⋅m=1 kg⋅m2/s2.
• The work done by a force is zero if the displacement is either zero or perpendicular to the force.
• The work done is positive if the force and displacement have the same direction, and negative if they have
opposite direction
Kinetic Energy and the Work-Energy Theorem
• The net work Wnet is the work done by the net force acting on an object.
• Work done on an object transfers energy to the object.
• The translational kinetic energy of an object of mass m moving at speed v is 𝐾𝐸 =1mv2/2
• The work-energy theorem states that the net work Wnet on a system changes its kinetic energy,
Wnet = 1mv2/2 -1mv2/2
Gravitational Potential Energy
• Work done against gravity in lifting an object becomes potential energy of the object-Earth system.
• The change in gravitational potential energy, ΔPEg, is ΔPEg=mgh, with h being the increase in height
and g the acceleration due to gravity.
• The gravitational potential energy of an object near Earth’s surface is due to its position in the mass-Earth
system. Only differences in gravitational potential energy, ΔPEg, have physical significance.
• As an object descends without friction, its gravitational potential energy changes into kinetic energy
corresponding to increasing speed, so that ΔKE= −ΔPEg.
Conservative Forces and Potential Energy
• A conservative force is one for which work depends only on the starting and ending points of a motion, not
on the path taken.
• We can define potential energy (PE) for any conservative force, just as we defined PEg for the
gravitational force.
• The potential energy of a spring is 𝑃𝐸𝑠 = 1kx2/2, where k is the spring’s force constant and x is the
displacement from its undeformed position.
, • Mechanical energy is defined to be KE+PE for a conservative force.
• When only conservative forces act on and within a system, the total mechanical energy is constant. In
equation form,
KE+PE=constant
or
KEi+PEi=KEf+PEf
where i and f denote initial and final values. This is known as the conservation of mechanical energy.
Power
Power is the rate at which work is done, or in equation form, for the average power P for work W done over
a time t, P=W/t.
The SI unit for power is the watt (W), where 1 W=1 J/s.
The power of many devices such as electric motors is also often expressed in horsepower (hp), where
1hp=746 W.
