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?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Topic Video
Question
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
PE
Uekstie
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
= sqrt( v
2 + ( (
V
m) -
) - (1/x
)) +
Take note that capital letters have different meaning than
small letter variables/constants.
![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:
PEm-- Amm, where A is a constant, m1 and m2 are the
masses of the two objects, and ris the distance between them.
Moreover, the new particle has an additional interaction with
the heavy particle through the following force expression
1 g0
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
KEIF+ KE2F + PEgravf + Uelasticf + Unewf = KE1 + KE2i +
] + Unewi
PEgravi *
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+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1148ac72-4c0c-4738-837a-a8c0132d6780%2F787d5645-0eab-4b67-855f-84eda98ac275%2Fmdheh6_processed.png&w=3840&q=75)
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:
PEm-- Amm, where A is a constant, m1 and m2 are the
masses of the two objects, and ris the distance between them.
Moreover, the new particle has an additional interaction with
the heavy particle through the following force expression
1 g0
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
KEIF+ KE2F + PEgravf + Uelasticf + Unewf = KE1 + KE2i +
] + Unewi
PEgravi *
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+
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON