Download WORK ENERGY THEOREM

WORK ENERGY THEOREM
According to the work-energy theorem, the net work on an object causes a change in the kinetic
energy of the object. The formula for net work is net work = change in kinetic energy = final kinetic
energy - initial kinetic energy.
The work W done by the net force on a particle equals the change in the particle's kinetic energy KE:
W=ΔKE= m
The work-energy theorem can be derived from
Newton's second law.
Work transfers energy from one place to another or
one form to another. In more general systems than the
particle system mentioned here, work can change
the potential energy of a mechanical device,
the heat energy in a thermal system, or the electrical
energy in an electrical device.
EK=
PE=mgh
The unit for work and energy is J
ME=mgh+
h=
; v= 2 ℎ
−
Examples:
1. Calculate the work needed to move an object in a distance of 8.3m using a force of 250N.
W=Fd=8.3m ∙ 250N=2075J
2. Find the distance travelled by an object with mass 45 kg moving at 22m/s acted on by a 100N
force.
F∙d= m
100d= (45)(484)
d=
=108.9m
3. Find the velocity at which a 55kg object is travelling when a 70N force acts on it over a distance
of 30m.
F∙d= m
70∙30= (55)(v2)
v2=
.
v=8.7m/s
4. Find the potential energy for a 27 kg object raised to a height of 15m.
PE=mgh
PE=27∙9.8∙15
PE=3969J
5. Find the velocity of an object just before it hits the ground, if it is dropped from a height of 23m.
v= 2 ℎ= 2(9.8)(23)=21.23m/s
6. Find the height from which an object falls if just before it hits the ground it has a velocity of
28m/s.
h= =
=40m
.
7. If an object hits the ground with a velocity of 16m/s, at what height did it have a velocity of
8m/s.
ME1=ME2
mgh1+
= mgh2+
v1=8m/s
2
h=?
2
m(gh1+ v1 )=m(gh2+ v2 )
gh1+ v12=gh2+ v22
h2is 0 because the object hits the ground.
v2=16m/s
gh1=
h1=
=
∙ .
=9.8m
8. Find the original height from which an object is dropped, if at a height of 40m it is moving at
20m/s.
gh1=gh2+ v2
2
gh1=(9.8)(40)+ (20)
h1=
. (
)
.
h1=?
h2=40m
v2=20m/s
=60.4m