The law of conservation of mechanical energy. TOPIC : The law of conservation of mechanical energy. How is kinetic energy defined?. Kinetic energy is defined as E k =1/2 mv 2. How is gravitational energy is defined?. Gravitational potential energy is defined as E pg =mgh.
The law of conservation of mechanical energy
TOPIC: The law of conservation of mechanical energy
How is kinetic energy defined?
Kinetic energy is defined as Ek =1/2 mv2
How is gravitational energy is defined?
Gravitational potential energy is defined as Epg =mgh
How is elastic potential energy is defined?
Kinetic energy is defined as Eps=1/2kx2
1 、 The concept of mechanical energy
Mechanical energy is total of Ek and Ep.
We can express it as E=Ek+Ep
(1) When an object is free fall
How does energy convert?
(2) When an object is thrown upward ,
what is the energy conversion?
(3) When the arrow is shot out by the bow,
what is the energy conversion?
A O B
Conclusion: kinetic energy and potential energy can be converted into each other.
3、 The concept of conservative forces
An object moves from point P to point Q along path1 or path2,
The work done by gravity is the same.
WG = mgh
The work done by elastic force is the same.
What conclusion can we come to according to the examples above?
A force is conservative force, if the work done by the force on an object moving between two points is independent of the path taken.
4、 The law of conservation of mechanical energy:
According to the theorem of kinetic energy ,
the work done by the resultant force equals the change of kinetic energy.
The resultant force is only gravity
W= mg (hi－hf ) (2)
The change of kinetic energy
△Ek= 1/2 mvf2－1/2mvi2 (3)
Hence mg (hi－hf )=1/2mvf2－1/2mvi2
Illustration: We get this equation by free fall motion. Similarly, either an object is in rectilinear motion or in curvilinear motion, only the work was done by gravity. We can always get the same conclusion.
This equation can be given :
E=Eki+Epgi =Ekf +Epgf
This is the law of conservation of mechanical energy.
It states that the total mechanical energy of a system remains constant if only gravity does works.
Similarly, if only the elastic force does work, the law of
conservation of mechanical energy can be given
or E=Eki +Epsi=Ekf+Epsf
Generally, if only conservative forces do work,
the law of conservation of mechanical energy states
the total mechanical energy of a system remains constant if the only force that does work is conservative force.
This is equivalent to the statement that
if the kinetic energy of a conservative system increases ( or decreases) by some amount , the potential energy must decrease ( or increase) the same amount.
It can be given E = Eki+∑Epi=Ekf + ∑Epf
Ekf - Eki = ∑Epi - ∑Epf
Example problem: A pendulum consists of a ball of mass 100g attached to a light cord of length 50cm. The ball is released near nose of a person from rest when the cord makes an angle 60° with the vertical ( ignoring air resistance)
(1)When the ball comes back, you predict what will happen?
( Can the ball hit the person’s nose?)
(2)Do this experiment and observe carefully the result of this experiment.
What is the result of this experiment?
(3) Explain the result of this experiment with the law of conservation of mechanical energy.
In the motion of the ball, two forces act on the ball. One is gravity and the other is the force of tension. Only gravity does work ( the direction of tension is perpendicular to the direction of the ball’s velocity, tension doesn’t do work), the mechanical energy is conserved. Its initial kinetic energy and its final kinetic energy are zero. The energy is entirely gravitational energy, so the ball comes back to original position a. As a result, the ball can’t hit the nose of the person.
B Calculation: What is the speed of the ball when it is at the lowest point b ?
We choose to take the zero potential energy at point b.
θ = 600
Vb = 2ghab
= 2g L (1- cos600 )
= 2 10 0.5 (1 – 0.5 ) m/s
= 5 m/s
According to the law of conservation of mechanical energy
hab =L –Lcosθ
6 Activity of students --------Ask and answer the
questions studied with each other .
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