Answer:
The fraction of kinetic energy lost in the collision in term of the initial energy is 0.49.
Explanation:
As the final and initial velocities are known it is possible then the kinetic energy is possible to calculate for each instant.
By definition, the kinetic energy is:
k = 0.5*mV^2
Expressing the initial and final kinetic energy for cars A and B:
[tex]ki=0.5*maVa_{i}^2+0.5*mbVb_{i}^2[/tex]
[tex]kf=0.5*maVa_{f}^2+0.5*mbVb_{f}^2[/tex]
Since the masses are equals:
[tex]m=ma=mb[/tex]
For the known velocities, the kinetics energies result:
[tex]ki=0.5*mVa_{i}^2[/tex]
[tex]ki=0.5*m(35 m/s)^2=612.5m^2/s^2*m[/tex]
[tex]kf=0.5*mbVb_{f}^2[/tex]
[tex]kf=0.5*m(25 m/s)^2=312.5m^2/s^2*m[/tex]
The lost energy in the collision is the difference between the initial and final kinectic energies:
[tex]kl=ki-kf[/tex]
[tex]kl = 612.5m^2/s^2*m-312.5 m^2/s^2*m=300 m^2/s^2*m [/tex]
Finally the relation between the lost and the initial kinetic energy:
[tex] kl/ki = 300 m^2/s^2 * m / 612.5 m^2/s^2 * m [/tex]
[tex]kl/ki = 24/49=0.49 [/tex]
Based on the data provided, the fraction of the initial kinetic energy is lost in the collision is 48.9%.
Momentum isbthe product of mass and velocity of a body.
From the principle of conservation of momentum, the momentum is conserved in an isolated system of colliding bodies.
Momentum before collision = Momentum after collision.
Kinetic energy = 1/2mv^2
Since the mass are the same, difference in kinetic energy s due to change in velocity.
Change in velocity = 25 - 35 = -10 m/s
Kinetic energy before collision = 1/2× 35 × 35 × m = 612.5m J
Kinetic energy after collision = 1/2 × 25 × 25 × m = 312.5 m J
Loss in Kinetic energy = 612.5m - 312.5m = 300m J
Fraction lost = 300m / 612.5 × 100 = 48.9%
Therefore, the fraction of the initial kinetic energy is lost in the collision is 48.9%.
Learn more about momentum and kinetic energy at: https://brainly.com/question/1468572
