Unit V: Gravitational and Elastic Potential Energy

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Questions and Answers

What type of energy is transformed into kinetic energy as a diver jumps from a high board?

  • Elastic potential energy
  • Chemical energy
  • Kinetic energy
  • Gravitational potential energy (correct)

What happens to gravitational potential energy as a body falls under the influence of gravity?

  • It increases
  • It remains constant
  • It decreases (correct)
  • It is converted to sound energy

Which statement is true about work done by gravitational force when a body moves upward?

  • The work done is negative (correct)
  • The work is always equal to the mass times gravitational acceleration
  • The work done is positive
  • The work done is zero

In the absence of air resistance, what can be said about the total mechanical energy of a freely falling body?

<p>It remains constant (A)</p> Signup and view all the answers

What is the relationship between work done by the gravitational force and kinetic energy change during free fall?

<p>Work done equals the change in kinetic energy (B)</p> Signup and view all the answers

Which type of potential energy is involved when a diver bends a diving board before jumping?

<p>Elastic potential energy (A)</p> Signup and view all the answers

If a body with mass m moves vertically downward, how is the work done by gravity expressed mathematically?

<p>W = mg(y1 - y2) (C)</p> Signup and view all the answers

What is the effect of adding other forces acting on a body moving vertically besides its weight?

<p>It changes the net work done on the body (C)</p> Signup and view all the answers

What expression represents the work done by the gravitational force during a displacement along a curved path?

<p>$W_{grav} = mgy_1 - mgy_2$ (D)</p> Signup and view all the answers

What is the relationship between kinetic energy and gravitational potential energy in a closed system?

<p>Total mechanical energy remains constant when ignoring air resistance. (C)</p> Signup and view all the answers

How does the work done by gravity vary with the path taken by an object between two points?

<p>It depends only on the vertical displacement between the two points. (C)</p> Signup and view all the answers

In which scenario is elastic potential energy relevant?

<p>A compressed spring acting on a mass. (C)</p> Signup and view all the answers

What happens to gravitational potential energy when an object is raised in a gravitational field?

<p>It increases with height. (B)</p> Signup and view all the answers

What is the correct expression for gravitational potential energy for a body at height $h$?

<p>$U_{grav} = mgh$ (C)</p> Signup and view all the answers

Which of the following statements about elastic potential energy is true?

<p>It is the energy stored when an elastic material is deformed. (A)</p> Signup and view all the answers

If a mass is attached to a spring and pulled to stretch it, what type of energy is being stored in the spring?

<p>Elastic potential energy (A)</p> Signup and view all the answers

What determines the change in total mechanical energy in a system where elastic and gravitational forces are acting?

<p>The work done by forces other than gravitational or elastic forces (D)</p> Signup and view all the answers

In the scenario of a trampoline jumper, how is gravitational potential energy affected as the jumper descends?

<p>It decreases. (B)</p> Signup and view all the answers

What is the effect of a positive work done by other forces on the total mechanical energy of the system?

<p>It increases the mechanical energy. (B)</p> Signup and view all the answers

When no work is done by forces other than gravitational and elastic forces, what happens to the total mechanical energy?

<p>It remains constant. (C)</p> Signup and view all the answers

How are elastic potential energy and gravitational potential energy related during a trampoline jump?

<p>Gravitational potential energy converts to elastic potential energy at the lowest point of the jump. (A)</p> Signup and view all the answers

Which equation correctly represents the relationship between work done by different forces and changes in kinetic energy?

<p>$W_{total} = K_2 - K_1$ (A)</p> Signup and view all the answers

What happens to the elastic potential energy when a jumper lands on a trampoline?

<p>It increases as kinetic energy decreases. (D)</p> Signup and view all the answers

What is the overall effect of the gravitational force on a mass that is both falling and attached to a spring?

<p>It impacts both kinetic and potential energy transformations within the system. (D)</p> Signup and view all the answers

Flashcards

Gravitational Potential Energy

Energy stored in an object due to its height above a reference point, and its weight.

Potential Energy

Energy associated with an object’s position or configuration.

Work done by weight

The work done by gravity on an object as it moves vertically; positive for downward motion, negative for upward motion.

Conservation of Mechanical Energy (Gravity)

When only gravity acts, the total mechanical energy (kinetic + potential) stays the same.

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Falling freely

An object is falling under the influence of only gravity, with no external forces (air resistance, etc.)

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Kinetic Energy

Energy associated with an object's motion.

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Mechanical Energy

The sum of kinetic and potential energy in a system

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Work - Energy Theorem

The total work done on an object is equal to its change of kinetic energy

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Work-Energy Theorem (Elastic Forces)

The total work done on an object is equal to its change in kinetic energy, considering work done by gravitational, elastic, and other forces.

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Total Work Done

The sum of the work done by gravitational force, elastic force, and any other forces acting on an object.

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Conservation of Mechanical Energy (Elastic Forces)

When only gravitational and elastic forces act on an object, the total mechanical energy (kinetic + potential) remains constant.

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Why Mechanical Energy isn't always conserved?

If other forces, besides gravity and elastic forces, do work on an object, the mechanical energy of the system changes.

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What is the 'system'?

The system includes the object (mass), the Earth (gravity), and the spring (elastic force) involved in the interaction.

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How does Wother affect E?

Positive Wother increases the total mechanical energy (E), while negative Wother decreases it.

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Trampoline jumping: Energy transformation

In trampoline jumping, energy transforms between kinetic energy, elastic potential energy (of the springs), and gravitational potential energy.

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Energy conversion in trampoline

When the jumper lands on the trampoline, some of the mechanical energy is converted into elastic potential energy stored in the springs.

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Energy Conservation Principle

When only conservative forces (like gravity) act on a system, the total mechanical energy (kinetic + potential) remains constant.

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Gravitational Potential Energy (Ugrav)

The energy an object possesses due to its position in a gravitational field. It's higher the farther the object is from the reference point.

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Work by Gravity (Wgrav)

The work done by the gravitational force on an object as it moves between two points. This only depends on the difference in height, not the path taken.

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What is Elastic Potential Energy?

Energy stored in a deformable object (like a spring or rubber band) when it's stretched or compressed. It's released when the object returns to its original shape.

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Equation for Work by Gravity

Wgrav = -mgy2 - mgy1 or Wgrav = mgy1 - mgy2, where m is mass, g is gravitational acceleration, and y1 and y2 are initial and final heights.

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Elastic Potential Energy (Uelastic)

The energy stored in an object due to its deformation – like a stretched spring. It's dependent on the spring constant and the deformation.

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How is Work Related to Kinetic Energy?

The total work done on an object equals its change in kinetic energy. This is called the Work-Energy Theorem.

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How is Work Related to Potential Energy?

The work done by a conservative force is equal to the negative change in potential energy. For example, Wgrav = -ΔUgrav.

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Study Notes

Unit V: Gravitational and Elastic Potential Energy

  • Unit V covers gravitational potential energy (7.1 to 7.5) and elastic potential energy.

  •  A diver jumping off a high board has gravitational potential energy, which transforms into kinetic energy as the diver falls. 

  •  If the diver bounces, the board stores elastic potential energy.

  •  Potential energy is the energy an object has due to its position.

  •  Gravitational potential energy is the energy an object has due to its height above a reference point.

  •  Raising an object to a higher height increases its gravitational potential energy.

  •  The work done by gravity increases a falling object's kinetic energy, as gravitational potential energy decreases.

  •  Gravitational potential energy (U grav) = m * g * y, where m is mass, g is acceleration due to gravity, and y is height.

  •  The work done by weight (W grav) = m * g * (y₁ - y₂), where y₁ is initial height and y₂ is final height.

  •  Suppose a body moves along the y-axis.

  •  Forces acting on the body are its weight (mg) and possibly other forces (F other).

  •  The work done by the weight as the body moves downward from y₁ to y₂ is W grav = mgy₁ - mgy₂.

  •  When the body moves upward, y₂ > y₁ and W grav is negative.

  •  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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