3.4 Conservation of Energy

• What type of energy is associated with an object's motion?

  Kinetic energy
• In mathematical terms, how is the Law of Conservation of Mechanical Energy expressed?

  E_{k1} + E_{p1} = E_{k2} + E_{p2}</latex>
• Mechanical energy is the sum of an object's kinetic energy and potential energy.
• The Law of Conservation of Mechanical Energy states that the total mechanical energy of an isolated system remains constant unless external forces do work on it.
• What is the formula for calculating kinetic energy?

  $\frac{1}{2}mv^{2}$
• The Conservation of Energy principle can be applied in simple systems to equate initial and final mechanical energy.

  True
• Kinetic energy depends on an object's mass and velocity.


  True
• Applying the Conservation of Energy requires no external forces to do work
• The Law of Conservation of Mechanical Energy states that in an isolated system, the total mechanical energy remains constant
• Potential energy is calculated using mass, gravitational acceleration, and height.

  True
• What is the potential energy of a 2 kg ball at a height of 5 m (assuming $g =$$9.8 \text{ m / s}^{2}$)?


  $98 \text{ J}$
• A 2 kg ball is dropped from a height of 5 m. What is its kinetic energy at the moment of impact with the ground?

  98 J
• What is the formula for potential energy?

  E_{p} = mgh
• The formula for potential energy is E_{p} = mgh
• A 2 kg ball is dropped from a height of 5 m. At impact, its kinetic energy is 98 J
• When a 2 kg ball is dropped from 5 m, its initial potential energy is fully converted to kinetic energy at impact.


  True
• Mechanical energy is the sum of an object's kinetic energy and potential energy.
• The Law of Conservation of Mechanical Energy states that the total mechanical energy of an isolated system remains constant as long as no external forces do work on the system.
• Understanding kinetic and potential energy is crucial for studying the Law of Conservation of Energy.


  True
• The Law of Conservation of Mechanical Energy applies only to isolated systems.


  True
• The total mechanical energy of an object is calculated using the formula E_{total} = E_{k} + E_{p}</latex>, where $E_{k}$ is kinetic energy and $E_{p}$ is potential energy.
• The total mechanical energy of an object is the sum of its kinetic energy and potential energy.
• Match the energy type with its formula:

  Kinetic Energy ↔️ \frac{1}{2}mv^{2}</latex>

  Potential Energy ↔️ $mgh$

  Total Mechanical Energy ↔️ $\frac{1}{2}mv^{2} +$$mgh$
• Total mechanical energy is calculated by adding kinetic and potential energy.


  True
• Understanding mechanical energy is crucial for studying the Law of Conservation of Energy.


  True
• Match the form of mechanical energy with its description:

  Kinetic Energy ↔️ Energy due to motion

  Potential Energy ↔️ Energy due to position or configuration
• What is the kinetic energy of an object with a mass of 2 kg and a velocity of 4 m/s?

  $16 \text{ J}$
• What principle is applied in the equation $E_{\pi} =$$E_{kf}$?


  Conservation of Energy
• The formula for initial kinetic energy is \frac{1}{2}mv_{i}^{2}
• Kinetic energy is the energy an object possesses due to its motion
• What two forms of energy make up mechanical energy?

  Kinetic and Potential
• In an isolated system with no external forces, initial mechanical energy equals final mechanical energy.


  True
• Steps to calculate the final kinetic energy of the ball in the example

  1️⃣ Calculate initial potential energy

  2️⃣ Apply conservation of energy

  3️⃣ Determine final kinetic energy
• The total mechanical energy of an isolated system remains constant.


  True
• Mechanical energy consists of two forms: kinetic energy and potential energy.
• What causes an object to possess potential energy?

  Its position
• Match the type of mechanical energy with its description:

  Kinetic Energy ↔️ Energy due to motion

  Potential Energy ↔️ Energy due to position
• What is the potential energy of a 2 kg object at a height of 3 meters?

  $58.8 \text{ J}$
• The total mechanical energy is the sum of kinetic energy and potential
• Potential energy depends on an object's mass, height, and gravitational acceleration