Physics Formula Energy

Physics Formula: Energy Concepts and Examples

Energy is a fundamental concept in physics, representing the ability to do work or produce change. Various forms of energy include kinetic, potential, thermal, chemical, and more. This article covers essential energy formulas, providing examples to illustrate their applications.

1. Kinetic Energy

Kinetic energy (\(KE\)) is the energy of motion. Any object in motion possesses kinetic energy, which is given by the formula:

\[ KE = \frac{1}{2}mv^2 \]

where:

• \(m\) is the mass of the object (in kilograms)
• \(v\) is the velocity of the object (in meters per second)

Example:

A car with a mass of 1000 kg is moving at a velocity of 20 m/s. The kinetic energy of the car is:

\[ KE = \frac{1}{2} \times 1000 \times 20^2 = \frac{1}{2} \times 1000 \times 400 = 200,000 \, \text{Joules (J)} \]

2. Potential Energy

Potential energy (\(PE\)) is the energy stored in an object due to its position or configuration. The most common type is gravitational potential energy, given by:

\[ PE = mgh \]

where:

• \(m\) is the mass of the object (in kilograms)
• \(g\) is the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\) on Earth)
• \(h\) is the height above the reference point (in meters)

Example:

A rock with a mass of 2 kg is at the edge of a cliff 50 meters high. The potential energy of the rock is:

\[ PE = 2 \times 9.8 \times 50 = 980 \, \text{J} \]

3. Thermal Energy

Thermal energy is the internal energy of an object due to the kinetic energy of its atoms and molecules. The change in thermal energy (\(\Delta Q\)) can be calculated using:

\[ \Delta Q = mc\Delta T \]

where:

• - \(m\) is the mass (in kilograms)
• - \(c\) is the specific heat capacity (in \(J/\text{kg}^\circ \text{C}\))
• - \(\Delta T\) is the change in temperature (in degrees Celsius)

Example:

Heating 2 kg of water (specific heat capacity \(4,186 \, \text{J/kg}^\circ \text{C}\)) from 20°C to 80°C:

\[ \Delta Q = 2 \times 4186 \times (80 - 20) = 2 \times 4186 \times 60 = 502,320 \, \text{J} \]

4. Work-Energy Principle

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy:

\[ W = \Delta KE = \frac{1}{2}m(v_f^2 - v_i^2) \]

where:

• \(W\) is the work done (in Joules)
• \(m\) is the mass (in kilograms)
• \(v_f\) is the final velocity (in meters per second)
• \(v_i\) is the initial velocity (in meters per second)

Example:

A 10 kg object is accelerated from 5 m/s to 15 m/s. The work done on the object is:

\[ W = \frac{1}{2} \times 10 \times (15^2 - 5^2) = \frac{1}{2} \times 10 \times (225 - 25) = \frac{1}{2} \times 10 \times 200 = 1,000 \, \text{J} \]

5. Conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In a closed system:

\[ E_{total\ initial} = E_{total\ final} \]

Example:

A roller coaster at the top of a 30 m hill (potential energy) converts its energy to kinetic energy as it descends. At the top:

\[ PE = mgh = m \times 9.8 \times 30 \]

At the bottom (height = 0, all potential energy converted to kinetic energy):

\[ KE = \frac{1}{2}mv^2 \]

Thus,

\[ m \times 9.8 \times 30 = \frac{1}{2}mv^2 \]

Solving for \(v\):

\[ 9.8 \times 30 = \frac{1}{2}v^2 \]

\[ 294 = \frac{1}{2}v^2 \]

\[ v^2 = 588 \]

\[ v \approx 24.26 \, \text{m/s} \]

Conclusion

Understanding energy and its various forms is fundamental in physics. These formulas for kinetic energy, potential energy, thermal energy, and work-energy principle are crucial for solving numerous practical problems. Mastery of these concepts enables one to analyze and predict the behavior of physical systems effectively.

Share :