Kinetic Energy: Its Relation with Movement and Velocity

Written on 19.03 by sianturikomkom

Kinetic Energy and Movement (Velocity).- To obtain the relation between energy and movement, let's imagine a particle of mass m moving in a straight line with initial velocity V_i . A net constant force F is then applied parallel to its movement, over a distance d. Then, the work done over the particle is W = Fd. As F = ma (a, acceleration) and using the kinetic energy formula V_f² = V_i² + 2ad, where V_f is the final velocity, we get:

W = Fd = mad = m[(V_f² - V_i²) / 2d]d
That is, W = ½mV_f² - ½mV_i²
It is clear we have a difference between final and initial quantities.
The kinetic energy (translational energy) of a particle is defined by physicists as the quantity ½mv² .
Ec = ½mv².
W can also be written
W = Ec
That is, the net work done on an object is equal to the change in his kinetic energy. This result is known as the work-kinetic energy theorem.
Let's notice W is the net work done over the object.
Example. Starting from rest, you push your 1.000 kg car over a 5 meters distance, on an horizontal ground, applying an also horizontal 400 N force. What is the car kinetic energy change?; What is its final velocity at the end of the 5 meters displacement? Disregard any friction force.
Solution. The change in kinetic energy must be equal to the net work done on the car,
W = Fd= (400 N)(5 m) = 2.000 J.
The final velocity is obtained from the equation
W = ½mV_f² - ½mV_i², where V_i = 0.
2.000 J = ( ½ )(1000 kg)V_f², from where V_f = 2 m/s.

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