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why does kinetic energy depend on half the square?
if we add up all the velocities does it not produce half a square?
if we add up all the velocities does it not produce half a square?
physdoc said:why does kinetic energy depend on half the square?
if we add up all the velocities does it not produce half a square?
Please explain further ...I am not familiar with the mechanics of calculus notation.drvrm said:imagine you are pushing a cart and produce a rate of change of displacement i.e. velocity and somebody says you have given K.E. to the cart by pushing through a force F.
now the work being done by you is F.dx if dx is displacement and F is related to change in velocity/momentum - so the energy input
you provided is m.dv/dt . dx for a small time dt involving displacement.
this can be written as m.dv/dx. dx/dt .dx so summing up for all such displacement = m.v.dv integrated from v=0 to v=v and that's the energy .with a factor of 1/2.m. v^2
physdoc said:Please explain further ...I am not familiar with the mechanics of calculus notation.
physdoc said:why does kinetic energy depend on half the square?
Kinetic energy is the energy that an object possesses due to its motion.
The formula for calculating kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.
Some examples of kinetic energy include a moving car, a person running, a spinning top, and a rolling ball.
Potential energy is the energy that an object possesses due to its position or state. When potential energy is converted into kinetic energy, the object begins to move.
The two main factors that affect an object's kinetic energy are its mass and velocity. The greater the mass and velocity, the greater the kinetic energy.