Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation...
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![Page 1: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/1.jpg)
Liceo Scientifico Isaac Newton
Physics course Potential Energy and
mechanical energy conservation
Professor
Serenella Iacino
Read by
Cinzia Cetraro
![Page 2: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/2.jpg)
1. Gravitational Potential energy
2. Elastic potential energy
Potential energy
![Page 3: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/3.jpg)
Gravitational potential energy represents the work done by gravity
fig.1
h P→m
W = P ∙ s = P ∙ h ∙ cos 0° = mgh
The Potential energy is indicated by the symbol U or only ( E P ).
→→
fig.2
m
hA
A
B
Bh
A B BAP→
W = m g h - m g h = U - U
![Page 4: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/4.jpg)
P→
mA
B
h=40m
fig.3
Let’s make an example:
W = U - U
m g h - m g h = U - U
m g 40 – 0 = 25000 from which
m g = = 625 N (this is the weight).
BAAB
BA B A
25000
40
![Page 5: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/5.jpg)
Gravitational potential energy depends only on the height h
h
CB
A
θ
s→
s→
h
CB
A
θ
s→
• the route ACB
• the vertical route AB
W = P s= P AB = P h cos0°=mghAB
∙→→
∙→ →
= P AC cos(90°- )+ P CBcos90°=
hsenθ
θsen
→
= mg = mgh
W = W + W = P AC + P CB =ACB AC CB ∙∙→ → →
θfig.5
fig.4
![Page 6: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/6.jpg)
N→
N→
P→
P→
s→
s→
Conservative force
vif
v >-1
2m v
f2 1
2m v
i2
W = > 0 from which
vif
v <-1
2m v
f2 1
2m v
i2
W = < 0 from which
fig.6
![Page 7: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/7.jpg)
m g h =1
2v
A
2m 1
2m g h = v
B
2m
N→
P→
s→
N→
P→
s→
A B
-1
2m v
f2 1
2m v
i2= 0
P→W = 0
fig.7
![Page 8: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/8.jpg)
Elastic potential energy of a compressed spring
U = 1
2K x
2
which represents the work done by the elastic force to pull the spring back towards its original length.
We can observe that the work depends only on the compression x and so on the initial and final positions of the spring, therefore the elastic force is a conservative force.However not all forces are conservative.
![Page 9: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/9.jpg)
Non conservative forces:
fig.8
s→ s→
s→
s→D C
A B
→Fa
→Fa
→Fa
→Fa
W = W + W + W + W = =DACDBCAB
- Fa
s- Fa
s - Fa
s - 4 Fa
s- Fa
s
Friction
![Page 10: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/10.jpg)
Mechanical Energy
E = U + K
the work – energy theorem:sum
= -1
2m v
f2 1
2m v
i2
W = K - Kf i
the difference in potential energy:
It is conserved only in systems where conservative forces are involved.
Wconservative force = U - U
i f
U - Ui f
K - Kf i
= U + Kf f
U + Ki i
=from which we have
Einitial = E
final
![Page 11: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/11.jpg)
highest point - highest gravitational potential energy
If there is no friction, the Roller Coaster is a demonstration of Energy Conservation.
Mechanical energy remains constant.
fig.9
![Page 12: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/12.jpg)
Spring and energy conservation
m
v→
fig.10
v→
fig.11
When the object compresses the spring, its kinetic energy decreases and is transformed into elastic potential energy.
m
When the motion is reversed, the potential energy decreases while the kinetic energy increases and when the object leaves the spring, the kinetic energy returns to its initial value.
![Page 13: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/13.jpg)
The pinball machine:
s→
fig.12
N→
P→
To fire the ball of mass m, suppose we compresse the spring, having a constant equal to K, by length x.Ignoring friction, we want to know what is the launch velocity of the ball.
U + Kf f
U + Ki i
=1
2K x
2 1
2v
f
2m+ 0 = 0 +
v f=
m
2K x m s
![Page 14: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/14.jpg)
Water Park:
h h
v 2
v 1
two children, two slides, no friction, same height h,
1
2v
1
2m+ 0 = 0 +m g h
1
2v
2
2m+ 0 = 0 +m g h
U + Kf f
U + Ki i
=
from which v =2
2 g hv 1= 2 g h and
![Page 15: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/15.jpg)
Conservative and non conservative forces:
sum=W Wcons Wnon cons+
sumW K - Kf i=
K - Kf i=Wcons Wnon cons+
Wcons= U - Ui f Wnon cons+U - Ui f K - Kf i=
Wnon cons U + Kf f U + Ki i= -
E initial-E finalWnon cons =
Law of energy conservation is no longer valid.
![Page 16: Liceo Scientifico Isaac Newton Physics course Potential Energy and mechanical energy conservation Professor Serenella Iacino Read by Cinzia Cetraro.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513c7e655034674748b4895/html5/thumbnails/16.jpg)
THE ENDenergy