This chapter explains the concepts of work, energy, and power, which are essential for understanding physical systems.
WORK, ENERGY AND POWER - Quick Look Revision Guide
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Essential formulas, key terms, and important concepts for quick reference and revision.
Key Points
Work is defined as W = F.d cos(θ).
Work is the product of force, displacement, and the cosine of the angle between them. If θ is 0°, work is positive; if it's 90°, no work is done.
Average power is defined as P = W/t.
Power measures how quickly work is done, calculated as total work done (W) divided by the time interval (t). The SI unit is the watt (W).
Kinetic Energy: K = 1/2 mv².
The kinetic energy of an object is dependent on its mass (m) and the square of its velocity (v). It's a scalar quantity that represents the work the object can perform due to its motion.
Work-Energy Theorem: ΔK = W.
The change in kinetic energy (ΔK) of a particle is equal to the net work done on it. This theorem applies to scenarios with varying forces.
Gravitational Potential Energy: V = mgh.
The potential energy (V) stored in an object due to its height (h) above a reference point is the product of its mass (m), gravitational acceleration (g), and height (h).
The conservation of mechanical energy states: K + V = constant.
In the absence of non-conservative forces, the total mechanical energy (sum of kinetic and potential energy) in a closed system remains constant.
Elastic and Inelastic Collisions.
In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, momentum is conserved, but kinetic energy is not.
Positive and Negative Work.
Work can be positive (force and displacement in the same direction) or negative (force and displacement in opposite directions).
Work done by a variable force requires integration.
For a varying force, work done is calculated as W = ∫ F(x) dx, which sums incremental work over displacement using calculus.
The Scalar Product: A·B = |A||B| cos(θ).
The dot product results in a scalar. It's dependent on the magnitudes of two vectors and the cosine of the angle between them.
Units of Work/Energy: 1 J = 1 N·m.
Work and energy share the same SI unit, joule (J), which is equivalent to one newton of force exerted over one meter of distance.
The spring force follows Hooke’s Law: F = -kx.
In ideal springs, the force (F) exerted by the spring is directly proportional to its extension (x) from its equilibrium position, where k is the spring constant.
Power has units of watts, where 1 W = 1 J/s.
Power quantifies the rate of energy use or work done, calculated via dividing work by time, highlighting efficiency and energy transfers.
Work done against friction is always negative.
Frictional forces oppose motion, leading to a decrease in kinetic energy, thus resulting in negative work being done on an object.
The work-energy theorem incorporates all forces.
This theorem states that the total work done by all forces acting on an object equals its change in kinetic energy, highlighting the connection between force and motion.
In closed systems, total momentum is conserved.
During collisions, the total momentum before and after remains constant, demonstrating a key principle in mechanics.
Terminal velocity is reached when forces balance.
An object in free fall stops accelerating when gravitational force equals resistive forces (like drag), leading to constant velocity.
Energy cannot be created or destroyed, only transformed.
The law of conservation of energy asserts that energy can change forms (like from potential to kinetic) but the total energy remains unchanged.
Friction converts kinetic energy to thermal energy.
In physical systems, kinetic energy is lost to friction, and this energy is often transformed into heat, affecting overall energy calculations.
Work done is path-independent for conservative forces.
In conservative fields, the work done on an object is only dependent on its initial and final positions, irrespective of the path taken.
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