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Old Jun 16th 2009, 12:19 PM   #1
s3a
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Kinetic/Potential Energies vs Distance --> Help needed please!

PHYSICS 534

Can someone please explain Exam 2006 #10 to me?

Any help would be greatly appreciated!
Thanks in advance!
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Old Jun 16th 2009, 01:44 PM   #2
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Answer is option A

Kinetic Energy=1/2mv^2

where v is the velocity of the body at any instant.
Now, using the equation of motion,
v^2=2ax

where x is the distance covered and a is the resultant acceleration of the object down the plane.
clearly, KE has linear dependence with x
so the graph of KE vs. Distance covered has to be a straight line.
Now, PE of the object=mgh where h is the height of the object.
we know that, h is proportional to the distance of the object from the ground
ie h=k(l-x) where l is the total length of the plane while x is the distance covered

k is a constant

so PE=kmg(l-x)
KE=max

so PE is a line with negative slope while KE is a line with positive slope
Now,
as half of the PE is lost in heat,sound,etc. the value of KE has to be less than the max. value of the PE[its initial value when the object was on top] when the object reaches the ground.
hence, A is the most appropriate option.

Last edited by Akshay; Jun 16th 2009 at 02:00 PM.
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Old Jun 16th 2009, 01:58 PM   #3
s3a
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Yes! Please explain!

Last edited by s3a; Jun 16th 2009 at 02:13 PM.
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Old Jun 16th 2009, 02:45 PM   #4
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Ok well I don't know some of the thing you said but from what I've understood:

Ek = (1/2)(m)(v^2) and Eg = mgh (Kinetic and Gravitational)

So I see how Eg = mgh, mass and gravity is constant while height is a variable and since gravity is negative, it'll make it a decreasing linear function.

What I don't understand is how Ek = (1/2)(m)(v^2) is not a quadratic since velocity is what varies and it is a squared variable. The reason why I believe that velocity is the variable is because it is accelerating downwards on the ramp.
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Old Jun 16th 2009, 11:08 PM   #5
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Yes, velocity does vary but the question asks the relationship between velocity and distance x

because the square of the velocity is a linear function of x

we know, that v^2=u^2+2ax

since u=0

v^2=2ax

hence KE=0.5mv^2=max

so KE is an increasing linear function of x.

it is the square of the velocity variable which is a linear function of x

square of velocity however, is a quadratic function of time

Last edited by Akshay; Jun 17th 2009 at 12:30 PM.
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