One newly discovered light particle has a mass of m and property q. Suppose it moves within the vicinity of an extremely heavy (fixed in place) particle with a property Q and mass M. When the light particle is xi distance from the heavy particle, it is moving directly away from the heavy particle with a speed of vi. a) What is the lighter particle's speed when it is xf away from the heavy particle?
One newly discovered light particle has a mass of m and property q. Suppose it moves within the vicinity of an extremely heavy (fixed in place) particle with a property Q and mass M. When the light particle is xi distance from the heavy particle, it is moving directly away from the heavy particle with a speed of vi. a) What is the lighter particle's speed when it is xf away from the heavy particle?
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One newly discovered light particle has a mass of m and property q. Suppose it moves within the vicinity of an extremely heavy (fixed in place) particle with a property Q and mass M. When the light particle is xi distance from the heavy particle, it is moving directly away from the heavy particle with a speed of vi. a) What is the lighter particle's speed when it is xf away from the heavy particle?
Transcribed Image Text:Since the heavy particle remains fixed, before and after the
motion of the lighter particle, it does not have any velocity,
moreover, there is no spring involved, so
KE1f +
+ Unewf =
+
+ Unewi
(Equation 1)
For all energies, we know the following
KE =
Am,m2
PEgrav
Uelastic
Unew = (1/
where in we have
m1 = m, m2 = M, q1 = q and q2 = Q
By substituting all these to Equation 1 and then simplifying
results to
2 + ( (
V
%3!
Aubs
Q
m ) -
) - (1/x
) +
Take note that capital letters have different meaning than
small letter variables/constants.
Transcribed Image Text:One newly discovered light particle has a mass of m and
property q. Suppose it moves within the vicinity of an
extremely heavy (fixed in place) particle with a property Q and
mass M. When the light particle is xi distance from the heavy
particle, it is moving directly away from the heavy particle with
a speed of vi. a) What is the lighter particle's speed when it is
xf away from the heavy particle?
Consider a new expression for gravitation potential energy as:
PE g"-
Am, m,
where A is a constant, m1 and m2 are the
masses of the two objects, and r is the distance between them.
Moreover, the new particle has an additional interaction with
the heavy particle through the following force expression
1 90
where , is a constant that is read as epsilon subscript 0, q
and Q are their new properties, r is the distance between the
new particle and the heavy particle.
Solution:
We may solve this using two approaches. One involves the
Newton's Laws and the other involving Work-Energy theorem.
To avoid the complexity of vector solution, we will instead
employ the Work-Energy theorem, more specifically, the
Conservation of Energy Principle.
Let us first name the lighter particle as object 1 and the heavy
particle as object 2.
Through work-energy theorem, we will take into account all of
the energy of the two-charged particle system before and after
traveling a certain distance as
KE1F + KE2F + PEgravf + Uelasticf + Unewf = KE1 + KE2i +
PEgravi *
|+ Unewi
Since the heavy particle remains fixed, before and after the
motion of the lighter particle, it does not have any velocity,
moreover, there is no spring involved, so
KE14 +
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