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Questions and Answers
What type of energy is transformed into kinetic energy as a diver jumps from a high board?
What type of energy is transformed into kinetic energy as a diver jumps from a high board?
What happens to gravitational potential energy as a body falls under the influence of gravity?
What happens to gravitational potential energy as a body falls under the influence of gravity?
Which statement is true about work done by gravitational force when a body moves upward?
Which statement is true about work done by gravitational force when a body moves upward?
In the absence of air resistance, what can be said about the total mechanical energy of a freely falling body?
In the absence of air resistance, what can be said about the total mechanical energy of a freely falling body?
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What is the relationship between work done by the gravitational force and kinetic energy change during free fall?
What is the relationship between work done by the gravitational force and kinetic energy change during free fall?
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Which type of potential energy is involved when a diver bends a diving board before jumping?
Which type of potential energy is involved when a diver bends a diving board before jumping?
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If a body with mass m moves vertically downward, how is the work done by gravity expressed mathematically?
If a body with mass m moves vertically downward, how is the work done by gravity expressed mathematically?
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What is the effect of adding other forces acting on a body moving vertically besides its weight?
What is the effect of adding other forces acting on a body moving vertically besides its weight?
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What expression represents the work done by the gravitational force during a displacement along a curved path?
What expression represents the work done by the gravitational force during a displacement along a curved path?
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What is the relationship between kinetic energy and gravitational potential energy in a closed system?
What is the relationship between kinetic energy and gravitational potential energy in a closed system?
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How does the work done by gravity vary with the path taken by an object between two points?
How does the work done by gravity vary with the path taken by an object between two points?
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In which scenario is elastic potential energy relevant?
In which scenario is elastic potential energy relevant?
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What happens to gravitational potential energy when an object is raised in a gravitational field?
What happens to gravitational potential energy when an object is raised in a gravitational field?
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What is the correct expression for gravitational potential energy for a body at height $h$?
What is the correct expression for gravitational potential energy for a body at height $h$?
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Which of the following statements about elastic potential energy is true?
Which of the following statements about elastic potential energy is true?
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If a mass is attached to a spring and pulled to stretch it, what type of energy is being stored in the spring?
If a mass is attached to a spring and pulled to stretch it, what type of energy is being stored in the spring?
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What determines the change in total mechanical energy in a system where elastic and gravitational forces are acting?
What determines the change in total mechanical energy in a system where elastic and gravitational forces are acting?
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In the scenario of a trampoline jumper, how is gravitational potential energy affected as the jumper descends?
In the scenario of a trampoline jumper, how is gravitational potential energy affected as the jumper descends?
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What is the effect of a positive work done by other forces on the total mechanical energy of the system?
What is the effect of a positive work done by other forces on the total mechanical energy of the system?
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When no work is done by forces other than gravitational and elastic forces, what happens to the total mechanical energy?
When no work is done by forces other than gravitational and elastic forces, what happens to the total mechanical energy?
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How are elastic potential energy and gravitational potential energy related during a trampoline jump?
How are elastic potential energy and gravitational potential energy related during a trampoline jump?
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Which equation correctly represents the relationship between work done by different forces and changes in kinetic energy?
Which equation correctly represents the relationship between work done by different forces and changes in kinetic energy?
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What happens to the elastic potential energy when a jumper lands on a trampoline?
What happens to the elastic potential energy when a jumper lands on a trampoline?
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What is the overall effect of the gravitational force on a mass that is both falling and attached to a spring?
What is the overall effect of the gravitational force on a mass that is both falling and attached to a spring?
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Study Notes
Unit V: Gravitational and Elastic Potential Energy
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Unit V covers gravitational potential energy (7.1 to 7.5) and elastic potential energy.
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A diver jumping off a high board has gravitational potential energy, which transforms into kinetic energy as the diver falls.
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If the diver bounces, the board stores elastic potential energy.
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Potential energy is the energy an object has due to its position.
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Gravitational potential energy is the energy an object has due to its height above a reference point.
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Raising an object to a higher height increases its gravitational potential energy.
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The work done by gravity increases a falling object's kinetic energy, as gravitational potential energy decreases.
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Gravitational potential energy (U grav) = m * g * y, where m is mass, g is acceleration due to gravity, and y is height.
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The work done by weight (W grav) = m * g * (y₁ - y₂), where y₁ is initial height and y₂ is final height.
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Suppose a body moves along the y-axis.
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Forces acting on the body are its weight (mg) and possibly other forces (F other).
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The work done by the weight as the body moves downward from y₁ to y₂ is W grav = mgy₁ - mgy₂.
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When the body moves upward, y₂ > y₁ and W grav is negative.
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Elastic potential energy is the energy stored in a deformed elastic object, like a stretched spring or a bent rubber band.
Conservation of Mechanical Energy
- If only gravity acts, then total mechanical energy (E = K + U grav ) is conserved.
- Example: A baseball thrown upward loses gravitational potential energy but gains kinetic energy; the sum remains constant (ignoring air resistance).
- If other forces also act, then total mechanical energy (E = K + U grav + U elastic + W other)= K + U grav changes.
When Forces Other than Gravity Do Work
- Total mechanical energy changes if forces other than gravity act.
- This work comes from additional forces like friction and pushing.
- Change in mechanical energy = work done by all forces.
Elastic Potential Energy
- Objects can store energy through deformation (like a stretched spring or rubber band).
- This is called elastic potential energy.
- Elastic potential energy is stored in elastic objects.
- Elastic potential energy (U el) = (1/2) * k * x², where k is the force constant and x is the deformation.
- If only the elastic force does work, then total mechanical energy is conserved (E = K + U elastic).
Application of Elastic Potential Energy
- Cheetah's back muscles and tendons store and release elastic potential energy during rapid acceleration and leaping.
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Description
This quiz explores the concepts of gravitational and elastic potential energy. It emphasizes how potential energy is related to an object's position, height, and how it transforms into kinetic energy during motion. Ideal for studying foundational physics concepts.
