Potential energy

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Apuntes de la lección

Definition of Potential Energy

Potential energy is energy that is stored in an object due to its position or shape.
Objects have potential energy because of their position (e.g., height) or shape (e.g., stretched or compressed).
A system is a set of parts that work together; a change in one part affects the others.

Types of Potential Energy

Gravitational potential energy is stored due to an object's height above a surface; the higher the object, the more gravitational potential energy it has.
Gravitational potential energy depends on the object's mass and its distance above the ground.
Elastic potential energy is stored when an object is stretched, compressed, or twisted and tends to return to its original shape.
Examples of elastic potential energy: stretched rubber bands, inflated balloons, compressed springs, and slingshots.

Examples of Potential Energy

A marble held at the top of a ramp has potential energy because it can roll down.
A brick lifted above the ground has gravitational potential energy.
A stretched elastic band has elastic potential energy.
Coal and other fuels store energy that can be released, so they have potential energy.
Batteries store energy for electric circuits, giving them potential energy.
Food contains stored chemical energy (potential energy) that our bodies use.

A boy holding a brick out at arm's length has given it potential energy; the brick on the ground has none.

Investigating Potential Energy

In the marble-ramp investigation, the higher the marble is placed, the further the cup moves, showing more potential energy at greater heights.
In the elastic band investigation, stretching the band more results in the matchbox moving further, indicating more elastic potential energy.
The amount of potential energy increases with greater distance (height or stretch) within a system.
Experiments show that more potential energy leads to more kinetic energy when released.

The marble-and-ramp setup: a foam cup with a hole faces a cardboard ramp propped at a measured height.

Energy Transfers and Conservation

Energy can be transferred from one object to another, e.g., from hand to elastic band to matchbox.
The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed or transferred.
After transfers, energy often becomes less available (e.g., as heat), but it is not lost.
In a falling brick example, the brick's potential energy converts to kinetic energy, then to heat and sound upon impact.

Measuring Energy

Energy is measured in joules (J); 1000 joules = 1 kilojoule (kJ).
The joule is named after physicist James Prescott Joule.
Food labels show energy content in kilojoules, indicating the potential energy stored in food.
Recommended daily energy intake varies by age, gender, and activity level (e.g., sedentary vs. active).

A nutritional information label showing energy content in kilojoules.

Potential Energy and Height

The higher an object is above a surface, the more gravitational potential energy it has.
A snowboarder at the top of a hill has the most potential energy; at the bottom, the least.
As a snowboarder descends, potential energy converts to kinetic energy (movement).
Data shows that higher hills lead to greater speeds because more potential energy becomes kinetic energy.

Two tennis balls at different heights above the ground, labeled A and B, to compare their potential energy.

Potential Energy in Systems

A system includes all interacting parts; energy transfers occur within and between systems.
Examples of systems: arm-brick-Earth, hand-elastic band-matchbox, skydiver-Earth.
In a kettle system, electrical energy is transferred to thermal energy to heat water.
Potential energy can be stored in various forms: gravitational, elastic, chemical, and nuclear.

A kettle plugged into a wall socket, illustrating a system where electrical energy is transferred.

Comparing Potential Energy

To compare potential energy, consider relative amounts based on position or shape.
A diver higher above the pool has more gravitational potential energy than one lower.
A rubber band stretched farther has more elastic potential energy than one stretched less.
In a roller coaster, the cart at the highest point has the most potential energy; at the lowest point, the least.

Two rock climbers at different heights on a rock face.

Key Questions and Concepts

Potential energy is the stored energy in a system.
Kinetic energy is the energy of motion.
Energy can be transferred and transformed but not created or destroyed.
Understanding potential energy helps explain phenomena like snowboarding speeds and why objects fall.

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Preguntas de práctica

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1.What is potential energy?
Easy
- AEnergy stored in an object due to its position or shape
- BEnergy of motion
- CEnergy transferred by heat
- DEnergy from the Sun
2.Which of the following is an example of potential energy?
Easy
- AA moving car
- BA stretched rubber band
- CA spinning top
- DA flying bird
3.What is the SI unit of energy?
Easy
- AJoule
- BNewton
- CWatt
- DKilogram
4.The higher an object is above a surface, the more gravitational potential energy it has.
Easy
True or false?
5.A compressed spring has no potential energy.
Easy
True or false?
6.Match each example to the type of potential energy it demonstrates.
Easy
- A book on a high shelf
- A stretched spring
- A compressed balloon
- Gravitational potential energy
- Elastic potential energy
- Elastic potential energy
7.Arrange the following objects in order of increasing gravitational potential energy, assuming the same mass:
Easy
- Object at 1 m height
- Object at 5 m height
- Object at 10 m height
8.Where does the high jumper have the most potential energy?
Easy
- AAt the top of the jump
- BJust after leaving the ground
- CJust before landing
- DAt the start of the run

Más preguntas

9.Where does the high jumper have the most kinetic energy?
Easy
- AAt the top of the jump
- BJust after leaving the ground
- CJust before landing
- DAt the start of the run
10.The high jumper has both potential and kinetic energy at some point during the jump.
Easy
True or false?
11.Arrange the following objects in order of increasing gravitational potential energy, assuming they are all at the same height above the ground.
Medium
- A 1 kg ball
- A 5 kg bowling ball
- A 2 kg brick
12.Which of the following are examples of objects that have elastic potential energy? (Select all that apply)
Medium
- AA stretched rubber band
- BAn inflated balloon
- CA book on a shelf
- DA compressed spring
- EA moving car
13.The higher an object is above the ground, the less gravitational potential energy it has.
Easy
True or false?
14.In the marble and ramp investigation, what happens to the distance the cup moves when the marble is released from a greater height?
Medium
- AThe cup moves less
- BThe cup moves more
- CThe cup moves the same distance
- DThe cup does not move
15.Which of the following correctly describes the energy transformation when a stretched elastic band is released and hits a matchbox?
Medium
- AKinetic energy → elastic potential energy
- BElastic potential energy → kinetic energy
- CGravitational potential energy → kinetic energy
- DKinetic energy → gravitational potential energy
16.Which of the following is the best experimental question to investigate how the height of a hill affects the speed of a snowboarder?
Medium
- AHow does the speed of the snowboarder affect the height of the hill?
- BHow does the type of snowboard affect the speed?
- CHow does the height of the hill affect the speed of the snowboarder?
- DHow does the hill affect the speed?
17.A student stretches a rubber band 2 cm, 4 cm, and 16 cm beyond its normal size. The distances the rubber band moved were 180 cm, 210 cm, and 420 cm respectively. Which statement best describes the pattern?
Easy
- AThe more the rubber band is stretched, the farther it moves when released.
- BThe less the rubber band is stretched, the farther it moves when released.
- CThe stretch of the rubber band has no effect on how far it moves.
- DThe rubber band moves the same distance regardless of stretch.
18.Which of the following factors affect the gravitational potential energy of an object? (Select all that apply)
Medium
- AThe mass of the object
- BThe height of the object above the ground
- CThe shape of the object
- DThe speed of the object
19.A stretched rubber band has elastic potential energy.
Easy
True or false?
20.Match each object to the type of potential energy it primarily stores.
Medium
- A book on a high shelf
- A compressed spring
- A skydiver just before jumping
- Gravitational potential energy
- Elastic potential energy
- Gravitational potential energy
21.Arrange the following positions of a roller coaster cart from least to greatest gravitational potential energy (assuming same mass and no other changes).
Medium
- At the bottom of the first hill
- At the top of the second hill (lower than the first)
- At the top of the first hill
22.A student investigates how the stretch of a rubber band affects the distance it moves when released. She collects data: stretch 2 cm → 180 cm, 4 cm → 210 cm, 16 cm → 420 cm. Which graph best represents the relationship between stretch and distance moved?
Medium
- AA line sloping upward from left to right
- BA line sloping downward from left to right
- CA horizontal line
- DA curve that goes up and then down
23.In the marble and ramp investigation, why is it important to keep the type of cup and the surface of the table the same?
Medium
- ATo ensure a fair test
- BTo make the experiment easier
- CTo increase the height of the ramp
- DTo make the marble roll faster
24.A student conducts the marble and ramp investigation and records the following distances for the cup movement: 5 cm height gives 8 cm, 10 cm height gives 15 cm, 15 cm height gives 21 cm. What is the most likely conclusion?
Medium
- AThe higher the marble is released, the further the cup moves.
- BThe higher the marble is released, the shorter the distance the cup moves.
- CThe height of the marble does not affect the distance the cup moves.
- DThe distance the cup moves is inversely proportional to the height.
25.In the elastic band investigation, a student stretches the band by 2 cm, 4 cm, and 8 cm. The distances the band moves are 180 cm, 210 cm, and 300 cm respectively. Which statement is best supported by this data?
Medium
- AIncreasing the stretch increases the distance the band moves, but not proportionally.
- BDoubling the stretch always doubles the distance.
- CThe distance moved is independent of the stretch.
- DThe distance moved decreases as the stretch increases.
26.In the marble and ramp investigation, the marble has potential energy because it is at a height above the table.
Medium
True or false?
27.In the elastic band investigation, the elastic band has potential energy only when it is released.
Medium
True or false?
28.What is the independent variable in this investigation?
Medium
- AHeight of ramp
- BDistance cup moves
- CMass of marble
- DType of cup
29.What is the dependent variable in this investigation?
Medium
- ADistance cup moves
- BHeight of ramp
- CMass of marble
- DType of cup
30.What is the independent variable?
Medium
- AStretch of elastic band
- BDistance matchbox moves
- CType of matchbox
- DLength of elastic band when unstretched
31.What is the dependent variable?
Medium
- ADistance matchbox moves
- BStretch of elastic band
- CType of matchbox
- DLength of elastic band when unstretched
32.Which of the following is an example of gravitational potential energy?
Easy
- AA book on a high shelf
- BA moving car
- CA stretched rubber band
- DA hot cup of tea
33.How many joules are in one kilojoule?
Easy
34.Complete the sentence:
Easy
Energy is measured in ____.
35.Complete the sentence.
Easy
The energy stored in an object due to its position or shape is called ____ energy.
36.A cereal box states that it contains 1500 kJ of energy per 100 g. How many joules is this?
Easy
37.What type of potential energy is stored in a stretched rubber band?
Medium
38.Complete the sentence: In the marble and ramp investigation, the independent variable is the ___ of the ramp.
Easy
In the marble and ramp investigation, the independent variable is the ____ of the ramp.
39.Explain why a snowboarder at the top of a higher hill has more potential energy than at the top of a lower hill.
Medium
40.Describe the energy transfer that occurs when a stretched elastic band is released and hits a matchbox.
Medium
41.Using Adeline's investigation data (hill height and speed), explain why a snowboarder on a small hill does not get as much speed as one who goes down a higher hill. Include evidence from the data.
Hard
42.Describe how you would improve the reliability of the marble and ramp investigation.
Medium
43.How many joules are in one kilojoule?
Easy
- A900 J
- B1100 J
- C1200 J
- D1000 J
44.A cereal box states that it contains 1500 kJ of energy per 100 g. How many joules is this?
Easy
- A1500000 J
- B1650000 J
- C1350000 J
- D1800000 J
45.Which cart has the most gravitational potential energy?
Medium
- ACart W
- BCart X
- CCart Y
- DCart Z
46.Which statement best compares the gravitational potential energy of cart X and cart Z?
Medium
- ACart X has less gravitational potential energy than cart Z because cart X has a smaller mass than cart Z.
- BCart X has more gravitational potential energy than cart Z because cart X has a greater speed than cart Z.
- CCart X has the same gravitational potential energy as cart Z because cart X is at the same height as cart Z.
- DCart X has the same gravitational potential energy as cart Z because cart X is made of the same material as cart Z.
47.Several objects sit on a set of shelves, as shown in the diagram. The mass of each object is given in the table. | Object | Mass (kg) | |---|---| | bowl | 0.40 | | school supply box | 0.95 | | rubber ball | 0.55 | | lunchbox | 1.10 | Which object has the largest gravitational potential energy relative to the floor?
Medium
- ABowl
- BLunchbox
- CRubber ball
- DSchool supply box
48.Students investigated a dropped marble at four drop heights. The table shows the height each marble was dropped from before it was released. | Height of drop (cm) | 12.5 | 25 | 50 | 100 | |---|---|---|---|---| Before each marble was dropped, at which height was the marble's potential energy the greatest?
Easy
- A12.5 cm, because potential energy increases as drop height increases
- B12.5 cm, because potential energy increases as drop height decreases
- C100 cm, because potential energy increases as drop height increases
- D100 cm, because potential energy increases as drop height decreases

Apuntes de repaso

## Potential Energy - Quick Revision ### Definition Potential energy is the energy stored in an object or system due to its position relative to other objects or the arrangement of its parts. It is equal to the work done against a restoring force (like gravity or a spring). The SI unit is the joule (J). ### Key Types - **Gravitational potential energy**: Stored due to height above a reference point. For an object of mass m at height h: \( U_g = mgh \) (g ≈ 9.8 m/s² on Earth) - **Elastic potential energy**: Stored in a deformed spring or elastic material. - **Chemical potential energy**: Stored in bonds between atoms/molecules (e.g., fossil fuels). - **Electric potential energy**: Stored due to position in an electric field. ### How It Works - Potential energy is associated with **conservative forces** (gravity, spring force). Work done by a conservative force depends only on start and end positions, not the path. - Work done against a force field **increases** potential energy; work done by the force field **decreases** it. - Formula: \( W = -\Delta U \) (negative sign means work done by the force reduces potential energy). ### Examples - Lifting a book: You do work against gravity → gravitational PE increases. - Stretching a rubber band: Work done against elastic force → elastic PE increases. - Dropping a ball: Gravitational PE converts to kinetic energy as it falls. ### Key Points - Potential energy is **stored energy** that can be converted to other forms (e.g., kinetic). - It is always measured relative to a reference position (e.g., ground level for gravity). - Common symbols: PE, U, V, Ep. ### History - Term coined by William Rankine in 1853. - Also called 'energy of configuration' (Rankine) vs. 'kinetic energy' (Thomson).

Potential energy: The energy stored in an object or system due to its position relative to other objects or the arrangement of its parts.
Gravitational potential energy: Potential energy due to an object's height above a reference point, calculated as U_g = mgh.
Elastic potential energy: Potential energy stored in a deformed elastic object, such as a stretched spring.
Conservative force: A force for which the work done depends only on the initial and final positions, not the path taken (e.g., gravity, spring force).
Joule: The SI unit of energy, symbol J.

Tarjetas

What is potential energy?

Potential energy is the energy stored in an object or system due to its position relative to other objects or the configuration of its particles.

What are common types of potential energy?

Common types include gravitational potential energy, elastic potential energy, and electric potential energy.

What is the SI unit for energy?

The SI unit for energy is the joule (symbol J).

Who coined the term 'potential energy'?

The term was coined by Scottish engineer and physicist William Rankine in 1853.

What is gravitational potential energy?

Gravitational potential energy is the energy stored due to an object's position in a gravitational field, given by U = mgh for an object of mass m at height h.

What is elastic potential energy?

Elastic potential energy is the energy stored in a deformed elastic object, such as a stretched or compressed spring.

How is potential energy related to work?

Work done against a conservative force increases potential energy; work done by the force decreases potential energy. Mathematically, W = -ΔU.

What are conservative forces?

Conservative forces are forces for which the total work done depends only on the initial and final positions, not on the path taken. Examples include gravity and elastic forces.

What is the formula for gravitational potential energy near Earth's surface?

U = mgh, where m is mass, g is acceleration due to gravity (about 9.8 m/s²), and h is height above a reference point.

How does stretching a spring affect its potential energy?

Stretching a spring increases its elastic potential energy because work is done against the restoring force of the spring.

What happens to gravitational potential energy when an object is lifted?

Lifting an object increases its gravitational potential energy because work is done against gravity.

What happens to potential energy when an object falls?

As an object falls, its gravitational potential energy decreases and is converted into kinetic energy.

Define conservative force field.

A conservative force field is a region where the force at each point is such that the work done moving between two points is path independent, and the force can be derived from a potential energy function.

What is the relationship between potential energy and force in a conservative field?

The force is the negative gradient of the potential energy: F = -∇U.

Why is potential energy considered 'stored energy'?

Potential energy is stored because it can be released and converted into other forms of energy, such as kinetic energy, when the object moves under the influence of a conservative force.

What is the reference position for potential energy?

Potential energy is defined relative to a reference position, often chosen as zero at a convenient point (e.g., ground level for gravity).

Give an example of potential energy in everyday life.

A book on a high shelf has gravitational potential energy; a drawn bow has elastic potential energy.

How does the mass of an object affect its gravitational potential energy?

Gravitational potential energy is directly proportional to mass (U = mgh), so a heavier object has more potential energy at the same height.

How does height affect gravitational potential energy?

Gravitational potential energy increases with height (U = mgh), so an object at a greater height has more potential energy.

What is the potential energy of an object at ground level if ground is the reference?

If ground level is chosen as the reference (h=0), then the gravitational potential energy is zero.

Can potential energy be negative?

Yes, potential energy can be negative if the reference point is chosen such that the object's position is below it.

What is the difference between potential energy and kinetic energy?

Potential energy is stored energy due to position or configuration, while kinetic energy is energy of motion.

How is potential energy related to the work done by an external force?

The work done by an external force against a conservative force is stored as potential energy.

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