- #1
ThievingSix
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In class it was explained that at half way between a given distance Potential energy(PE) lost equals the Kinetic energy(KE) gained. OR
PE Lost = KE Gained at 1/2 the distance.
But when i do the math for it, it does not work out. What am i missing, i understand the concept but i can't prove it? And in theory it sounds correct because of the law of conservation of energy.
Here is the situation(i made it up to prove that the statement is correct).
[PLAIN]http://img854.imageshack.us/img854/3959/diagram.png
This is what i have so far,
Distance = 1m
Time = 1s
Mass = 10kg
Acceleration = 9.8 m/s/s
Initial speed = 0 m/s
Final speed = 9.8 m/s
Force = 98N(toward's the center of the earth)
Gravitational Potential energy(mass*gravity*height) = 10*9.1*1 = 98 kgms
Potential energy at rest(mass*acceleration*displacement) = 10*9.8*1 = 98 kgms
Kinetic energy at rest(1/2 Mv2) = 1/2*10*0 = 0 kgms
This is where it gets confusing,
PE at "X" = 10*9.8*0.5(half the displacement) = 49 kgms(which should be correct)
KE at "X" = 1/2*10*4.92(velocity at "X") = 120.05 kgms
Therefore PE lost [tex]\neq[/tex] KE gained at half the distance?
I've done something wrong, but what?, I've ran through this so many times i can't even see my own error.
PE Lost = KE Gained at 1/2 the distance.
But when i do the math for it, it does not work out. What am i missing, i understand the concept but i can't prove it? And in theory it sounds correct because of the law of conservation of energy.
Here is the situation(i made it up to prove that the statement is correct).
A stationary mass is dropped from a distance of 1m and the only force that acts upon it is the Earth's gravity, it hits the ground in 1 second and its motion is along the Y axis only. Calculate PE and KE at "X".
[PLAIN]http://img854.imageshack.us/img854/3959/diagram.png
This is what i have so far,
Distance = 1m
Time = 1s
Mass = 10kg
Acceleration = 9.8 m/s/s
Initial speed = 0 m/s
Final speed = 9.8 m/s
Force = 98N(toward's the center of the earth)
Gravitational Potential energy(mass*gravity*height) = 10*9.1*1 = 98 kgms
Potential energy at rest(mass*acceleration*displacement) = 10*9.8*1 = 98 kgms
Kinetic energy at rest(1/2 Mv2) = 1/2*10*0 = 0 kgms
This is where it gets confusing,
PE at "X" = 10*9.8*0.5(half the displacement) = 49 kgms(which should be correct)
KE at "X" = 1/2*10*4.92(velocity at "X") = 120.05 kgms
Therefore PE lost [tex]\neq[/tex] KE gained at half the distance?
I've done something wrong, but what?, I've ran through this so many times i can't even see my own error.
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