,PHY1505 Assignment 4 (COMPLETE ANSWERS)
2024 - DUE September 2024 ; 100% TRUSTED
Complete, trusted solutions and explanations.
1. A ball drops some distance and loses 30 J of gravitational
potential energy. Do NOT ignore air resistance. How much
kinetic energy did the ball gain?
Understanding Gravitational Potential Energy and Kinetic
Energy
When a ball drops from a height, it converts gravitational
potential energy (GPE) into kinetic energy (KE). The relationship
between these two forms of energy is governed by the
principle of conservation of energy. However, in this scenario,
we must consider that air resistance is acting on the ball, which
affects the total energy conversion.
Step 1: Define Gravitational Potential Energy Loss
The problem states that the ball loses 30 J of gravitational
potential energy. This means that as the ball falls, it converts
some of its stored gravitational potential energy into kinetic
energy.
Step 2: Consider Air Resistance
Air resistance acts against the motion of the falling ball,
meaning not all of the lost gravitational potential energy will
convert into kinetic energy. Some of this energy is dissipated as
heat due to air friction. Therefore, we cannot directly equate
the loss in GPE to an equal gain in KE.
,Step 3: Establishing Energy Relationships
In an ideal situation without air resistance, if a ball loses 30 J of
GPE, it would gain exactly 30 J of KE. However, with air
resistance present, we can express this relationship as:
KE gained=GPE lost−Energy lost to air resistance
Given that we do not have specific information about how
much energy was lost to air resistance in this case, we cannot
determine an exact value for the kinetic energy gained without
additional data.
Conclusion
Since we know that the ball loses 30 J of GPE but do not have
information on how much was lost to air resistance, we cannot
definitively state how much kinetic energy was gained. The
maximum possible gain in kinetic energy would be less than or
equal to 30 J depending on the amount dissipated due to air
resistance.
Thus, without further information regarding the effects of air
resistance on this specific drop:
The answer is indeterminate based on provided information;
however, if no significant loss occurred due to air resistance,
then: 0 J < KE gained ≤ 30 J.
Top 3 Authoritative Sources Used in Answering this Question
1. Physics Classroom
, A comprehensive online resource for physics education
that explains concepts such as gravitational potential and
kinetic energies clearly and accurately.
2. HyperPhysics
An educational website hosted by Georgia State University
that provides detailed explanations and diagrams related
to physics topics including mechanics and energy
transformations.
3. Khan Academy
An educational platform offering free courses and
resources covering various subjects including physics; it
provides clear explanations about concepts like potential
and kinetic energies along with real-world applications.
When a ball drops and loses gravitational potential energy,
it converts that energy into kinetic energy. However, since
you mentioned not ignoring air resistance, some of the
potential energy is lost to air resistance instead of being
converted to kinetic energy.
In this case, the ball lost 30 J of gravitational potential
energy, but due to air resistance, it does not gain all of that
energy as kinetic energy. The actual kinetic energy gained
would be less than 30 J.
If you want to find out how much kinetic energy the ball
gained, you would need to know how much energy was lost
to air resistance. Without that information, we can't
determine the exact amount of kinetic energy gained, but it
will be less than 30 J.
2024 - DUE September 2024 ; 100% TRUSTED
Complete, trusted solutions and explanations.
1. A ball drops some distance and loses 30 J of gravitational
potential energy. Do NOT ignore air resistance. How much
kinetic energy did the ball gain?
Understanding Gravitational Potential Energy and Kinetic
Energy
When a ball drops from a height, it converts gravitational
potential energy (GPE) into kinetic energy (KE). The relationship
between these two forms of energy is governed by the
principle of conservation of energy. However, in this scenario,
we must consider that air resistance is acting on the ball, which
affects the total energy conversion.
Step 1: Define Gravitational Potential Energy Loss
The problem states that the ball loses 30 J of gravitational
potential energy. This means that as the ball falls, it converts
some of its stored gravitational potential energy into kinetic
energy.
Step 2: Consider Air Resistance
Air resistance acts against the motion of the falling ball,
meaning not all of the lost gravitational potential energy will
convert into kinetic energy. Some of this energy is dissipated as
heat due to air friction. Therefore, we cannot directly equate
the loss in GPE to an equal gain in KE.
,Step 3: Establishing Energy Relationships
In an ideal situation without air resistance, if a ball loses 30 J of
GPE, it would gain exactly 30 J of KE. However, with air
resistance present, we can express this relationship as:
KE gained=GPE lost−Energy lost to air resistance
Given that we do not have specific information about how
much energy was lost to air resistance in this case, we cannot
determine an exact value for the kinetic energy gained without
additional data.
Conclusion
Since we know that the ball loses 30 J of GPE but do not have
information on how much was lost to air resistance, we cannot
definitively state how much kinetic energy was gained. The
maximum possible gain in kinetic energy would be less than or
equal to 30 J depending on the amount dissipated due to air
resistance.
Thus, without further information regarding the effects of air
resistance on this specific drop:
The answer is indeterminate based on provided information;
however, if no significant loss occurred due to air resistance,
then: 0 J < KE gained ≤ 30 J.
Top 3 Authoritative Sources Used in Answering this Question
1. Physics Classroom
, A comprehensive online resource for physics education
that explains concepts such as gravitational potential and
kinetic energies clearly and accurately.
2. HyperPhysics
An educational website hosted by Georgia State University
that provides detailed explanations and diagrams related
to physics topics including mechanics and energy
transformations.
3. Khan Academy
An educational platform offering free courses and
resources covering various subjects including physics; it
provides clear explanations about concepts like potential
and kinetic energies along with real-world applications.
When a ball drops and loses gravitational potential energy,
it converts that energy into kinetic energy. However, since
you mentioned not ignoring air resistance, some of the
potential energy is lost to air resistance instead of being
converted to kinetic energy.
In this case, the ball lost 30 J of gravitational potential
energy, but due to air resistance, it does not gain all of that
energy as kinetic energy. The actual kinetic energy gained
would be less than 30 J.
If you want to find out how much kinetic energy the ball
gained, you would need to know how much energy was lost
to air resistance. Without that information, we can't
determine the exact amount of kinetic energy gained, but it
will be less than 30 J.
