Work, Energy and Power
Why This Matters
This lesson introduces the fundamental concepts of work, energy, and power, which are crucial for understanding how forces cause motion and how energy is transformed and transferred. We will explore the definitions, calculations, and interrelationships between these quantities, laying the groundwork for more advanced mechanics topics.
Key Words to Know
Work Done
Work done (W) is a scalar quantity defined as the product of the force (F) applied to an object and the displacement (s) of the object in the direction of the force. Mathematically, it is given by:
W = Fs cosθ
where θ is the angle between the force vector and the displacement vector.
- If the force is in the direction of displacement (θ = 0°), cosθ = 1, so W = Fs.
- If the force is opposite to the direction of displacement (θ = 180°), cosθ = -1, so W = -Fs (work done by the object or against the force).
- If the force is perpendicular to the displacement (θ = 90°), cosθ = 0, so W = 0 (no work done by that force).
The SI unit for work done is the Joule (J), where 1 J = 1 Nm. Work done represents the energy transferred. Positive work done means energy is transferred to the object, while negative work done means energy is transferred from the object.
Kinetic Energy and Gravitational Potential Energy
Energy is the capacity to do work. We will focus on two key forms of mechanical energy:
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Kinetic Energy (KE): This is the energy an object possesses due to its motion. It is given by the formula:
KE = 1/2 mv²
where m is the mass of the object and v is its speed. KE is always a positive scalar quantity.
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Gravitational Potential Energy (GPE): This is the energy an object possesses due to its position in a gravitational field. It is given by the formula:
GPE = mgh
where m is the mass, g is the acceleration due to gravity (approximately 9.81 m/s² on Earth), and h is the vertical height above a chosen reference point. GPE is a scalar quantity and can be positive or negative depending on the reference point. The change in GPE is usually what is important.
Elastic Potential Energy
Elastic potential energy (EPE) is the energy stored in an elastic object, such as a spring, when it is stretched or compressed. For an ideal spring obeying Hooke's Law (F = kx), the EPE is given by:
EPE = 1/2 kx²
where k is the spring constant (a measure of the spring's stiffness, in N/m) and x is the extension or compression from its equilibrium position.
- The spring constant 'k' represents the force required per unit extension/compression.
- This formula assumes the elastic limit of the material is not exceeded. Beyond the elastic limit, the material undergoes permanent deformation, and the relationship F=kx no longer holds.
- EPE is always a positive scalar quantity, as energy is stored regardless of whether the spring is stretched or compressed.
Principle of Conservation of Energy
The Principle of Conservation of Energy is one of the most fundamental laws in physics. It states that energy cannot b...
Power and Efficiency
Power (P) is defined as the rate at which work is done or energy is transferred. It is a scalar quantity given by:
P ...
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Exam Tips
- 1.Always state the principle of conservation of energy clearly when using it in calculations, and identify any non-conservative forces present.
- 2.Pay close attention to the direction of forces and displacements when calculating work done. A negative sign indicates work done *against* the force.
- 3.Remember that GPE depends on the *change* in height; choose a sensible reference level (h=0) to simplify calculations.
- 4.Distinguish carefully between work done, energy, and power. Work and energy are measured in Joules (J), while power is measured in Watts (W).
- 5.When solving problems involving springs, ensure you use the extension/compression 'x' from the equilibrium position, not the total length.