WORK, ENERGY, AND
ENERGY CONSERVATION
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-> any activity that requires muscular or mental effort
-> done by exerting force on an object w/c then undergoes
displacement
-> requires energy
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-> any activity that requires muscular or mental effort
-> done by exerting force on an object w/c then undergoes
displacement
-> requires energy
W F d
θ
Fd cos θ
θ
W F||d Fd|| 𝑑
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W F d
θ
Fd cos θ
θ
W F||d Fd||
-> SI unit – joule (J) after James Prescott Joule 1J 1 N m
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𝜃
𝜃
𝜃
d
Work is done ON the body
W (positive) Work is done BY the one exerting force on the body
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θ θ
θ
d
W (negative) Work is done BY the body
Work is done ON the one exerting force on the body
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d
W 0
Zero work done
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d
d
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d
Gravity is really the one doing the work!
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A farmer hitches her tractor to a sled loaded with firewood and
pulls it a distance of 20 m along level ground (Fig. 6.7a). The to
tal weight of sled and load is 14,700 N. The tractor exerts a con
stant 5000-N force at an angle 36.9°of above the horizontal. A
3500-N friction force opposes the sled’s motion. Find the work
done by each force acting on the led and the total work done
by all the forces.
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A factory worker pushes a 30.0-kg crate a distance of 4.5 m
along a level floor at constant velocity by pushing horizontally
on it. The coefficient of kinetic friction between the crate and th
e floor is 0.25.
(a)What magnitude of force must the worker apply?
(b)How much work is done on the crate by this force?
(c) How much work is done on the crate by friction?
(d)How much work is done on the crate by the normal force?
By gravity?
(e)What is the total work done on the crate?
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QUIZ
A 75.0-kg painter climbs a ladder that is 2.75 m
long leaning against a vertical wall. The ladder
makes a angle 30.0° with the wall. How much
work does gravity do on the painter?
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QUIZ ANSWER
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We can conclude that when a particle undergoes a
displacement,
• it speeds up if 𝑊𝑡𝑜𝑡 > 0
• slows down if 𝑊𝑡𝑜𝑡 < 0 and
• maintains the same speed if 𝑊𝑡𝑜𝑡 = 0.
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-> energy due to motion (speed)
1 2
K mv
2
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-> energy due to motion (speed)
Work-Energy Theorem for Kinetic Energy
1 2
K mv Wtot K K f Ki
2
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Work-Energy Theorem for Kinetic Energy
Wtot K K f K i
𝑲𝒇 > 𝑲𝒊 𝑲𝒇 < 𝑲 𝒊 𝑲 𝒇 = 𝑲𝒊
it speeds up slows down maintains the same
speed
𝑊𝑡𝑜𝑡 > 0 𝑊𝑡𝑜𝑡 < 0 𝑊𝑡𝑜𝑡 = 0
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POTENTIAL ENERGY
-> energy associated with position (gravitational,
elastic, electric)
-> potential (possibility) of work to be done
U g mgy gravitational potential energy
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U g mgy
Work-Energy theorem for
gravitational potential energy
Wg U g
U gi U gf
work done by gravity
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U g mgy
Work-Energy theorem for
gravitational potential energy
Wg U g
U gi U gf
work done by gravity
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-> potential energy for an elastic object (i.e. spring, rubber band)
elastic force required to stretch or compress a
F kx spring a distance x
1 2 elastic potential energy associated for a spring
U e kx
2
Work-Energy theorem for elastic potential energy
We U e
U ei U ef work done by a spring
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d
d d
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MECHANICAL ENERGY-> total energy of a system (kinetic + potential)
E K U
Principle of Conservation of Mechanical Energy
-> mechanical energy of the system doesn’t change
Ei E f
K i U gi U ei K f U gf U ef
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If there are other forces (other than gravity and elastic force)
present, mechanical energy is not conserved
Ki U gi U ei Wother K f U gf U ef
general work-energy theorem
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-> a force that offers a two-way conversion between kinetic
and potential energies
-> gravitational force, elastic force PE
-> doesn’t depend on the path,
only on the initial and final position
Ei E f KE
K i U gi U ei K f U gf U ef
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Non-Conservative Forces
-> dissipative force (causes mechanical energy to be lost)
-> frictional force
Ki U gi U ei Wother K f U gf U ef
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Check your understanding!
A rock dropping
(both kinetic and potential)
A vehicle moving on a horizontal line
(Kinetic only)
A coin at rest on the level ground
(neither kinetic nor potential)
An elevator standing at the 5th floor
(Potential only)
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Applications
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Thank You!
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