Law of Conservation of Energy:
- The law of conservation of energy is that energy cannot be created nor destroyed it can only be transferred and stored in other objects.
Mathematical representation of the law of conservation of energy:
- Abbreviated version: Ei=Ef
- Extended Version: GPEi+SPEi+KEi+PGEf+SPEf+KEf
Units of Energy:
- SI units: Joules
- American Units: Calories and BTU
Video and Explanation:
a.
b.Energy is conserved in a roller coaster as shown in the video, it carries a
relationship between both potential and kinetic energy. The roller coaster has both
potential and kinetic energy because when the roller coaster goes up it has potential
energy and when it travels down it has kinetic energy. When the roller coaster goes
at the top of the loop it uses gravitational energy to go down. The conservation of
energy is traded off between both types of energies.
relationship between both potential and kinetic energy. The roller coaster has both
potential and kinetic energy because when the roller coaster goes up it has potential
energy and when it travels down it has kinetic energy. When the roller coaster goes
at the top of the loop it uses gravitational energy to go down. The conservation of
energy is traded off between both types of energies.
Problems:
- Use the law of conservation of energy (assume no friction) to fill in the blanks at the various marked positions for a 1000-kg roller coaster car.
a.450,000 =1000*9.8*h
h=45.9 m
b. KE=0 J
v=0 m/s
c. KE + PE =450,000 J
KE = 250,000 J
d. 200,000=1000*9.8*h
h = 20.4 m
e. 250,000=0.5*1000*v^2
v=22.4 m/s
f. KE+PE=450,000 J
KE=450 000 J
g. the height is 0 m
PE = 0 J
h. 500,000=0.5*1000*v^2
v = 31.6 m/s
i. a=g*sin angle
a = 7.07 m/s/s
2. Brenda is 68 kg, she’s riding her skateboard down a 16 m hill, she is moving at 2 m/s.
What’s her final velocity?
Known (mvi^2/2)+mghi+(mvf^2/2)+mgh2
M=68 kg (68 x 0)/2+(68 x 9.8 x 16)=(68 x v^2)/2
H=16 m 21,324.8 = (68 x v^2)/2)2
G=9.8 m/s^2 2 x 21,324.8 = (68 x v^2)
Vi=o m/s 42,649.6 =(68 x v^2)
Unknown 42,649.6 /68=v^2
Vf=? 25.04=vf
What’s her final velocity?
M=68 kg (68 x 0)/2+(68 x 9.8 x 16)=(68 x v^2)/2
H=16 m 21,324.8 = (68 x v^2)/2)2
G=9.8 m/s^2 2 x 21,324.8 = (68 x v^2)
Vi=o m/s 42,649.6 =(68 x v^2)
Unknown 42,649.6 /68=v^2
Vf=? 25.04=vf
X-games loop:
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| There is only potential energy because no movement has occurred yet which means that the energy is stored. 0 m/s because its at rest. |
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| There is more potential energy than kinetic because there's nothing but gravity pulling the skater down.
mgh1=mgh2 + mv^2 / 2 →gh1-gh2=(v^2) / 2→(9.8) (8) - (9.8) (3.5) = (v^2) / 2→78.4 - 34.3 = (v^2) / 2→2 (44.1)=(v^2)/2(2)→√88.2)=√(v^2)→v=9.39 m/s
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| There more kinetic energy because there's movement since the skater went down the ramp.
mvi /2+mgh1=mgh2+mvf^2 / 2 → mgh1 = mvf^2/2 → gh1 = vf^2/2 → (9.8)(8)=vf^2/2 → (78.4)2=(vf^2/2)2 → 156.8=vf^2→ vf=√156.8 →12.52 m/s
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