Glossary

is the energy of motion, calculated as half the product of and squared. It's a key concept in understanding how objects move and interact, playing a crucial role in collisions, , and power calculations.

isn't fixed—it changes based on an object's reference frame and can convert to other energy forms. This ties into the broader principle of , where total energy in a closed system remains constant, even as it shifts between different types.

Kinetic Energy

Kinetic energy calculation

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  • Represents energy possessed by an object due to its motion
    • Calculated using formula KE=12mv2KE = \frac{1}{2}mv^2, mm is mass and vv is velocity
  • Depends on object's mass and velocity
    • Doubling mass doubles kinetic energy (2 kg object moving at 1 m/s has 2 J of KE)
    • Doubling velocity quadruples kinetic energy (1 kg object moving at 2 m/s has 4 J of KE)
  • Also calculated using (pp)
    • Formula KE=p22mKE = \frac{p^2}{2m}, [p = mv](https://www.fiveableKeyTerm:p_=_mv)
    • 2 kg object with momentum of 4 kg⋅m/s has 4 J of KE
  • Measured in joules (J) in SI units
    • 1 J = 1 (kinetic energy of 1 kg object moving at 1 m/s)
  • Related to through force and acceleration
    • F=maF = ma can be used to determine change in kinetic energy over time

Kinetic energy in reference frames

  • Relative quantity depends on frame of reference
    • Stationary ball on a moving train has KE relative to the ground
  • states physics laws are same in all
    • Velocity is relative but velocity differences between frames are absolute
  • Two frames A and B with relative velocity [vAB](https://www.fiveableKeyTerm:vAB)[v_{AB}](https://www.fiveableKeyTerm:v_{AB})
    • Object velocity vAv_A in frame A is vB=vA−vABv_B = v_A - v_{AB} in frame B
    • KE in frame B is KEB=12m(vA−vAB)2KE_B = \frac{1}{2}m(v_A - v_{AB})^2
    • Ball thrown 10 m/s on train moving 20 m/s has KE of 45 J relative to ground
  • Applies to objects in

Applications of kinetic energy

  • Total energy conserved in closed system during collisions and interactions
    • KE can convert to potential, thermal, or other forms
  • conserve kinetic energy
    1. Ball bouncing on hard floor retains most of its KE after each bounce
    2. KEinitial=KEfinalKE_{initial} = KE_{final}
  • convert some KE to other forms
    1. Two clay balls stick together after colliding, losing KE to deformation
    2. KEinitial>KEfinalKE_{initial} > KE_{final}
  • relates work done to change in KE
    • W=ΔKE=12mvf2−12mvi2W = \Delta KE = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2, WW is work, viv_i and vfv_f are initial and final velocities
    • Pushing 1000 kg car from rest to 10 m/s requires 50,000 J of work
  • Power is rate of doing work or transferring energy
    • P=dWdt=ddt(12mv2)P = \frac{dW}{dt} = \frac{d}{dt}(\frac{1}{2}mv^2), PP is power, tt is time
    • 100 W motor can give 1 kg object KE of 50 J in 0.5 s

Energy Conservation and Mechanical Energy

  • Kinetic energy is a component of
  • In a closed system, total (kinetic + potential) remains constant
  • principle applies to all forms of energy, including kinetic
  • Work done on an object changes its mechanical energy

Key Terms to Review (26)

Elastic Collisions: Elastic collisions are a type of collision between two or more objects where the total kinetic energy of the system is conserved. This means that the sum of the kinetic energies of the colliding objects before the collision is equal to the sum of their kinetic energies after the collision.
Energy conservation: Energy conservation is the principle stating that the total energy in an isolated system remains constant over time. Energy can neither be created nor destroyed, only transformed from one form to another.
Energy Conservation: Energy conservation is the fundamental principle that states the total energy of an isolated system is constant; it is said to be conserved over time. This means that energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another.
Galilean Relativity: Galilean relativity is a principle in classical physics that states the laws of mechanics are the same in all inertial frames of reference. It establishes that the motion of an object is relative to the observer, and that there is no absolute or preferred frame of reference.
Inelastic Collisions: An inelastic collision is a type of collision where the colliding objects stick together after the impact, resulting in a change in their kinetic energy. In this type of collision, the total momentum is conserved, but the total kinetic energy is not conserved due to the loss of energy in the form of heat, sound, or other forms of energy.
Inertial Frames: An inertial frame of reference is a frame of reference in which an object at rest remains at rest, and an object in motion continues to move at a constant velocity, unless acted upon by an external force. It is a fundamental concept in classical mechanics and special relativity.
Joule: A joule is the SI unit of work or energy, equivalent to one newton-meter. It represents the amount of work done when a force of one newton displaces an object by one meter in the direction of the force.
Joule: The joule (J) is the standard unit of energy in the International System of Units (SI). It represents the amount of work done or energy expended when a force of one newton acts through a distance of one meter.
Kg⋅m²/s²: kg⋅m²/s² is a unit of measurement that represents energy or work. It is the product of mass (kg), distance squared (m²), and the inverse of time squared (1/s²), which simplifies to Joules (J), the standard unit of energy.
Kinetic energy: Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass and velocity of the object.
Kinetic Energy: Kinetic energy (KE) is the energy of motion possessed by an object. It is directly proportional to the mass of the object and to the square of its velocity, as described by the formula KE = p^2/2m, where p is the object's momentum and m is its mass.
Mass: Mass is a fundamental physical quantity that represents the amount of matter in an object. It is a measure of an object's resistance to changes in its state of motion, and it is a key concept in the study of mechanics and the behavior of objects under the influence of forces.
Mechanical energy: Mechanical energy is the sum of kinetic energy and potential energy in a system. It is the energy associated with the motion and position of an object.
Mechanical Energy: Mechanical energy is the sum of the kinetic energy and potential energy possessed by an object due to its motion and position within a physical system. It represents the total energy available to do work or cause change in the system.
Momentum: Momentum is a vector quantity that describes the motion of an object. It is defined as the product of an object's mass and its velocity, and it represents the object's quantity of motion. Momentum is a fundamental concept in physics that is closely related to other important topics such as forces, energy, and collisions.
Net work: Net work is the total work done on an object, accounting for all forces acting on it. It determines the change in the object's kinetic energy.
Newton's Second Law: Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. It describes the relationship between an object's motion and the forces acting upon it, providing a quantitative framework for understanding the dynamics of physical systems.
P = dW/dt: P = dW/dt is a fundamental equation that describes the relationship between power (P), the rate of change of work (dW/dt), and time. It is a key concept in the study of energy, work, and the transfer of energy between different forms.
P = mv: The equation p = mv, where p represents linear momentum, m represents mass, and v represents velocity, is a fundamental relationship in physics that connects the concepts of kinetic energy and linear momentum. This equation describes the quantity of motion possessed by an object, which is a crucial factor in understanding the dynamics of physical systems.
Translational Motion: Translational motion refers to the movement of an object from one location to another without any rotation or change in orientation. It is the most basic form of motion, where the object's center of mass follows a linear path through space.
V_{AB}: The relative velocity between two objects, A and B, is denoted as $v_{AB}$. It represents the speed and direction of the motion of object B relative to the frame of reference of object A. This term is particularly important in the context of understanding kinetic energy, as the relative velocity between objects is a crucial factor in determining the kinetic energy of a system.
Velocity: Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both the speed and the direction of an object's motion, making it a more complete description of an object's movement compared to just speed alone.
W = ΔKE: The work (W) done on an object is equal to the change in the object's kinetic energy (ΔKE). This relationship expresses the fundamental principle that the work done on an object results in a change in its kinetic energy, which is the energy an object possesses due to its motion.
Work: Work is a physical quantity that describes the energy transferred by a force acting on an object as the object is displaced. It is the product of the force applied and the displacement of the object in the direction of the force.
Work-energy theorem: The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. Mathematically, it is expressed as $W_{net} = \Delta KE$.
Work-Energy Theorem: The work-energy theorem is a fundamental principle in physics that states the change in the kinetic energy of an object is equal to the net work done on that object. It establishes a direct relationship between the work performed on an object and the resulting change in its kinetic energy, providing a powerful tool for analyzing and solving problems involving energy transformations.
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