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Mechanical Energy

Website: Young Education
Kurs: Work Energy Power
Buch: Mechanical Energy
Gedruckt von: ゲストユーザ
Datum: Freitag, 25. September 2026, 02:37

Inhaltsverzeichnis

1. Kinetic Energy

Learning outcomes
  • I can define kinetic energy as the energy associated with motion.
  • I can explain how an object's mass and speed affect its kinetic energy.
  • I can recall and use the equation\( E_k = \frac{1}{2}mv^2 \) .
  • I can calculate the kinetic energy of moving objects in a variety of situations.
  • I can analyze how changes in speed affect kinetic energy and explain why kinetic energy increases rapidly with velocity.

Kinetic Energy

The amount of kinetic energy in a moving object can be calculated using the equation: 

Ek=½m v2 

where

  • Ek is measured in joules (J) 
  • m is mass measured in kilograms (kg)
  • v is speed measured in metres per second (m/s) 

An apple of mass 100 g falls from a tree. It reaches a speed of 6 m/s before landing on Isaac’s head. What is the gain of kinetic energy of the apple? 

List:

  • m = 100g = 0.1kg
  • v = 6 m/s
  • E = ?

Equation:

Ek=½m v2 

Solve:

E = 0.5(0.1)(6)2

E = 1.8J

 

..

2. Gravitational Potential Energy

Learning outcomes
  • I can define gravitational potential energy as energy stored due to position in a gravitational field.
  • I can explain how mass, height, and gravitational field strength affect gravitational potential energy.
  • I can recall and use the equation ΔEp = mgΔh.
  • I can calculate changes in gravitational potential energy for objects raised or lowered vertically.
  • I can relate changes in gravitational potential energy to real-world systems such as roller coasters, dams, and falling objects.

Potential Energy

The amount of gravitational potential energy stored by an object at height can be calculated using the equation: 

Ep=mg h

where

  • Ep is measured in joules (J) 
  • m mass, is measured in kilograms (kg) 
  • g is gravitational field strength, measured in newtons per kilogram (N/kg) 
  • h is height,  measured in metres (m) 

Galileo takes a 5 kg cannonball to the top of the Tower of Pisa for one of his experiments. The tower is 56 m high. How much gravitational potential energy has the cannonball gained? (g = 10 N/kg) 

List:

  • h = 56m
  • g = 10 N/kg
  • m = 5 kg

Equation:

E = mgh

Solve:

E = 5(10)(56)

E = 2800 J

Potential Energy

Elastic potential energy is the energy stored in a spring, given by the equation:

EH=½m x2

Kinetic and Potential Energy Worksheet.pdf 

3. Elastic Potential Energy

Learning outcomes
  • I can define elastic potential energy as energy stored when an object is stretched or compressed.
  • I can describe situations in which elastic potential energy is stored and released.
  • I can explain how elastic potential energy depends on deformation and spring stiffness.
  • I can recall and use the equation Ee = ½kx2 
  • I can calculate elastic potential energy in springs and other elastic systems.

E = .5kx^2

  1. A spring (k = 7.50 N/m) has been stretched 0.40 m from its equilibrium position. What is the potential energy now stored in the spring?
  2. A spring (k = 800 N/m) has been compressed, and 196 J of potential energy is stored. What distance from equilibrium has the spring been compressed?
  3. Calculate the spring constant of a spring that stores 100J of energy when compressed 500cm.
  4. A spring has 900J of energy applied to it. It has a spring constant of 20N/m. Calculate the extension.
  5. A spring has 900J of energy applied to it. It has a spring constant of 20,000 N/m. Calculate the extension.
  6. How much work must be done on a spring with a spring constant of 80 N/m to stretch the spring 20 cm?
  7. A spring has an extension of 20 cm. Calculate the elastic potential energy stored in the spring (k = 100 N/m).
  8. A spring is stretched with a spring constant of 3 N/m until it is extended by 50 cm. What is the elastic potential energy stored by the spring?
  9. How much elastic potential energy does a spring store when it is compressed by 0.2 m if it has a spring constant of 5 N/m?
  10. What is the elastic potential energy stored in a spring whose spring constant is 160 N/m when it is compressed 8.0 cm? 
  11. How much would a spring scale with a spring constant of 120 N/m stretch if it had 3.75J of work done on it?
  12. What is the spring constant of a spring if the extension of the spring is 0.15 m when 0.72J of potential energy is stored in it?

4. Conservation of Mechanical Energy

Learning outcomes
  • I can explain the principle of conservation of mechanical energy.
  • I can describe how kinetic, gravitational potential, and elastic potential energy can be transformed into one another.
  • I can apply conservation of mechanical energy to determine unknown speeds, heights, or energies.
  • I can analyze energy changes in systems such as roller coasters, pendulums, and spring launchers.
  • I can explain how friction and air resistance affect the conservation of mechanical energy.

5. Energy Transformations and Calculations

Learning outcomes
  • I can identify multiple energy transformations occurring within a physical system.
  • I can construct energy flow diagrams to represent mechanical energy changes.
  • I can solve multi-step problems involving kinetic, gravitational potential, and elastic potential energy.
  • I can analyze systems that involve both energy conservation and energy dissipation.
  • I can evaluate real-world situations by tracking energy transfers and transformations throughout a process.