08 Energy

 


Learning Outcomes

  • Solve problems involving work and energy in marine contexts; and
  • Solve problems involving conservation of mechanical energy

Energy in Physics and Marine Biology

Introduction to Energy

In physics, energy is the ability to do work. It exists in various forms, such as kinetic energy (energy of motion) and potential energy (stored energy). Energy can be transferred between objects or converted from one form to another, but the total amount of energy remains constant. This concept is known as the conservation of energy.

For marine biology, understanding energy is important in studying the movement of marine organisms, the energy requirements for their survival, and how energy flows through marine ecosystems.

Types of Mechanical Energy

1. Kinetic Energy (KE): The energy an object possesses due to its motion. The faster an object moves, the more kinetic energy it has. The formula for kinetic energy is:

KE = (1/2) ​mv2

Where:

  • m is the mass of the object (in kilograms, kg),
  • v is the velocity of the object (in meters per second, m/s),
  • KE is the kinetic energy (in joules, J).

2. Potential Energy (PE): The energy stored in an object because of its position or state. One common type is gravitational potential energy, which depends on the height of the object relative to a reference point. The formula for gravitational potential energy is:

PE = mgh

Where:

  • m is the mass of the object (in kilograms, kg),
  • g is the acceleration due to gravity (9.8 m/s²),
  • h is the height of the object (in meters, m).

Use of Kinetic Energy in Marine Biology Research

Kinetic energy (KE) plays a significant role in marine biology research. Understanding how organisms and equipment move through water is essential for studying species' behavior, migration patterns, and energy efficiency in marine ecosystems. 

Researchers often calculate the kinetic energy of marine species like tuna or whale sharks to gain insight into their movement and energy expenditure during swimming. This helps in understanding how animals interact with their environment, such as how they hunt or evade predators, and informs conservation efforts by analyzing energy consumption over long migrations. 

Additionally, kinetic energy calculations are crucial in the design and operation of underwater drones and other marine research tools. By studying these devices' movement through water, scientists can optimize energy usage and improve the efficiency of data collection in the field. 

The following problems illustrate how kinetic energy can be calculated for various marine organisms and research equipment, emphasizing its practical applications in marine biology.


Sample Problem 1: Calculating Kinetic Energy of a Moving Fish

A tuna, with a mass of 50 kg, is swimming at a speed of 4 m/s. How much kinetic energy does the tuna have?

Given:
Mass (m) = 50 kg
Velocity (v) = 4 m/s

Find: KE

Solution:

KE = (1/2)​mv2 = (1/2) ​× 50 kg × (4m/s)2 = 400 J

The tuna has 400 joules of kinetic energy.

Sample Problem 2: Calculating Kinetic Energy of a Whale Shark

A whale shark with a mass of 20,000 kg is moving at a speed of 2 m/s. Calculate its kinetic energy.

Given:
Mass (m) = 20,000 kg
Velocity (v) = 2 m/s

Find: KE

Solution:

KE = (1/2)​mv2 = (1/2) ​× 20,000 kg × (2 m/s)2 = 40,000 J

The whale shark has 40,000 joules of kinetic energy.


Sample Problem 3: Kinetic Energy Problem (Mass from F = ma)

In a marine research vessel, a small underwater drone exerts a force of 400 N to accelerate a mass from rest over 4 seconds. The acceleration of the drone is measured at 2 m/s². Calculate the mass of the drone and its kinetic energy after 4 seconds.

Given:

F = 400 N
a = 2 m/s²
t = 4 s
vo = 0

Find: m, KE

Solution:

  1. Calculate the mass using Newton's second law:

    F = ma  ⟹  m = F/a = 400/ 2=200 kg

  2. Use the kinematic equation to find the final velocity after 4 seconds:

    v = vo + at = 0 + (2)(4) = 8 m/s

  3. Calculate the kinetic energy:

    KE = (1/2)mv2 = (1/2)(200)(8)2 = 6,400 J

The drone’s kinetic energy after 4 seconds is 6,400 J.


Sample Problem 4: Kinetic Energy Problem (Velocity from Kinematic Equations)

A marine biologist tags a sea turtle with a GPS tracker. The turtle, starting from rest, accelerates at a constant rate of 0.5 m/s² and travels 50 meters over a coral reef. Calculate the turtle's velocity after traveling this distance and determine its kinetic energy if the turtle's mass is 150 kg.

Given:

vo= o
a = 0.5 m/s²
d = 50 m
m = 150 kg

Find: v, KE

Solution:

  1. Use the kinematic equation to calculate the velocity:

    v2=vo2 + 2ad = 0 + 2(0.5)(50) ≈7.07 m/s

  2. Calculate the kinetic energy:

    KE = (1/2)mv2 = (1/2)(150)(7.07)2 = 3,750 J

The kinetic energy of the sea turtle after traveling 50 meters is approximately 3,750 J.

Energy in Marine Ecosystems: Tidal Energy

Marine ecosystems are powered by various forms of energy, one of the most important being tidal energy. Tidal currents move vast amounts of water, and this kinetic energy can be harnessed to generate electricity. Understanding how to capture and convert this kinetic energy into electrical energy requires knowledge of both potential and kinetic energy, as well as conservation of energy principles.

In areas like Camiguin Island, tidal energy has the potential to be a sustainable energy source for coastal communities. Researchers are studying how the energy of moving water can be used to power homes and businesses, reducing the need for fossil fuels.


Sample Problem 5: Energy in Tidal Currents

A tidal turbine is placed in a water current moving at 3 m/s. The turbine blades have a mass of 500 kg. Calculate the kinetic energy of the water moving through the turbine blades.

Given:
Mass (m) = 500 kg
Velocity (v) = 3 m/s

Find: KE

Solution:

Using the kinetic energy formula:

KE = (1/2)​mv2 = (1/2) ​× 500 kg × (3 m/s)2 = 2,250 J

The water moving through the turbine blades has 2,250 joules of kinetic energy.

Practice Problems: Kinetic Energy

  1. A boat engine provides a constant force of 1,000 N to move a 2,000 kg boat through the water at 2 m/s. What is the kinetic energy of the boat

  2. A marine biologist tracks a dolphin that swims at a speed of 8 m/s. If the dolphin has a mass of 150 kg, calculate its kinetic energy.
  3. Kinetic Energy Problem (Mass from F = ma): A marine survey boat uses a propeller to exert a force of 1,200 N on a diver propulsion vehicle (DPV), resulting in an acceleration of 3 m/s². Calculate the mass of the DPV and its kinetic energy after it has been accelerating for 5 seconds.
  4. Kinetic Energy Problem (Velocity from Kinematic Equations): A research team studies a manta ray swimming in open water. The manta ray accelerates uniformly from rest at 0.3 m/s² over a distance of 60 meters. If the manta ray’s mass is 250 kg, calculate its velocity after 60 meters and its kinetic energy at that point.
  5. Kinetic Energy Problem (Mass from F = ma): An underwater ROV (Remotely Operated Vehicle) exerts a thrust force of 2,000 N while experiencing an acceleration of 2.5 m/s². Determine the ROV’s mass and calculate its kinetic energy after reaching a velocity of 10 m/s.
  6. Kinetic Energy Problem (Velocity from Kinematic Equations): A marine biologist observes a blue whale accelerating from rest at 0.2 m/s² over a distance of 80 meters. If the whale's mass is 50,000 kg, calculate its velocity after 80 meters and determine its kinetic energy.

The Role of Potential Energy in Marine Biology Research

In marine biology, understanding the concept of gravitational potential energy (PE) is crucial for studying the dynamics of various organisms and objects in aquatic environments. 

Gravitational potential energy, which depends on an object’s mass, gravitational acceleration, and its height relative to a reference point, is particularly relevant when examining the movement of marine life, equipment, and buoyant objects in the water. 

In research scenarios, marine biologists frequently calculate PE to assess energy changes in systems involving organisms like giant clams, divers, or buoyant objects, which are affected by gravitational forces and displacement underwater. 

This concept helps researchers understand the energy required for movement in aquatic ecosystems, aiding in the design of marine technologies and the conservation of marine life.


Sample Problem 1: Calculating Potential Energy of a Giant Clam

A giant clam with a mass of 250 kg is 3 meters below the surface of the water. How much gravitational potential energy does it have relative to the water surface?

Given:
Mass (m) = 250 kg
Height (h) = 3 m
Gravity (g) = 9.8 m/s²

Find: PE

Solution:

PE = mgh = 250 kg × 9.8 m/s2 × 3 m = 7,350 J

The giant clam has 7,350 joules of gravitational potential energy.


Sample Problem 2: Potential Energy Problem (Mass from F = ma)

A diver explores an underwater cliff and experiences a gravitational force of 980 N due to her weight. If her acceleration due to gravity is 9.8 m/s2, calculate her mass and the potential energy at a depth of 30 meters below the surface.

Given:

F = 980 N
a = g = 9.8 m/s2
h = 30 m

Find: m, PE

Solution:

  1. Calculate the mass using F=maF = maF=ma:

    F = ma  ⟹  m = F/a =980/9.8 = 100 kg

  2. Calculate the potential energy:

    PE = mgh = (100)(9.8)(30) = 29,400 J

The diver's potential energy at 30 meters below the surface is 29,400 J.


Sample Problem 3: Potential Energy Problem (Height from Kinematic Equations)

A marine biologist releases a buoyant object from the ocean floor. The object accelerates upward at a constant rate of 0.4 m/s². If it reaches the surface in 10 seconds, calculate the total height the object has traveled and its potential energy when it reaches the surface. The object’s mass is 20 kg.

Given

a = 0.4 m/s²

t = 10 s

m = 20 kg

Find: h, PE

Solution:

  1. Use the kinematic equation to calculate the height (displacement):

    h = d = vot + (1/2)at2 = 12(0.4)(10)2 = 12(0.4)(100) = 20 m

  2. Calculate the potential energy:

    PE = mgh = (20)(9.8)(20) =3,920 J

The potential energy of the object at the surface is 3,920 J.

Practice Problems: Potential Energy

  1. A 70 kg diver jumps from a boat into the water and reaches a depth of 5 meters. Calculate the gravitational potential energy of the diver before the jump.
  2. A seabird drops a shellfish from a height of 10 meters to break it on the rocks below. If the shellfish weighs 0.5 kg, how much potential energy does it have before it falls?
  3. Potential Energy Problem (Mass from F = ma): A research vessel drops an anchor that experiences a downward force of 1,960 N. If the acceleration due to gravity is 9.8 m/s2, calculate the mass of the anchor and its potential energy when it is lifted to a height of 20 meters above the seabed.
  4. Potential Energy Problem (Height from Kinematic Equations): A buoy starts from rest and is pulled upward with an acceleration of 0.3 m/s² for 12 seconds. If the buoy has a mass of 50 kg, calculate the height it travels and its potential energy when it reaches this height.
  5. Potential Energy Problem (Mass from F = ma): A marine biology team hoists a sample cage from the seafloor. The cage experiences a force of 4,900 N due to gravity. If the gravitational acceleration is 9.8 m/s2, calculate the mass of the cage and the potential energy when it is lifted 15 meters off the seafloor.
  6. Potential Energy Problem (Height from Kinematic Equations): A deep-sea diver retrieves an artifact from a shipwreck at a depth of 35 meters. The object accelerates upward at 0.5 m/s² over 10 seconds. Calculate the height traveled by the object and its potential energy if its mass is 12 kg.
  7. Potential Energy Problem (Height from Kinematic Equations): A marine biologist releases a buoy from rest, and it accelerates upward at 0.2 m/s² for 15 seconds. Calculate the height the buoy reaches and its potential energy if the buoy’s mass is 30 kg.
  8. Potential Energy Problem (Height from Kinematic Equations): A diving bell starts at rest and is pulled upward by a cable with an acceleration of 0.4 m/s². After traveling for 25 seconds, calculate the height the bell rises and the potential energy if the mass of the bell is 500 kg.


Energy plays a fundamental role in marine biology, from the movement of organisms to the functioning of ecosystems. Whether it's the kinetic energy of marine animals or the potential energy of objects in the water column, understanding energy helps scientists better predict the behavior and needs of marine life. Conservation of energy principles also guide research into sustainable energy sources like tidal power, showing how marine environments can contribute to global energy solutions.

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