Answer to Question #116231 in Mechanics | Relativity for Rethabile Force

Question #116231
A car with a mass of 1565 kg initially at rest accelerates at a constant rate with a time interval of 9.2s reaches 12 m/s. It then collides with a stationary car with an elastic spring bumper.
What's the final kinetic energy of the system?
Expert's answer

Explanations & Calculations

  • As the collision starts, total energy the system (moving car & the stationary car) has is the kinetic energy which is gained by the moving car.
  • Since the collision is elastic due to the spring being elastic, no kinetic energy is absorbed.
  • And as no any information is given regarding the external frictional forces from the surroundings there is no any means of losing energy of the system.
  • Therefore, final kinetic energy of the system equals to that which was just before the collision gained by the car in motion.
  • What happens after the collision is that, the two cars move in different velocities in a way the system's momentum is kept constant.

Therefore, the kinetic energy (also the final) of the system is,

"\\qquad\\qquad\n\\begin{aligned}\n\\small E_k &= \\small \\frac{1}{2}mv^2\\\\\n&= \\small \\frac{1}{2}\\times1565kg\\times (12ms^{-1})^2\\\\\n&= \\small \\bold{112680\\,J}\\\\\n&= \\small \\bold{112.68\\,kJ}\n\\end{aligned}"

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