Coriolis\' alternative method for finding work can be used to estimate the relat

Question

Coriolis' alternative method for finding work can be used to estimate the relative stopping distance for a car given the car's speed. For this application of Coriolis' alternative method, the force of friction is in the opposite direction of the motion of the car on which that frictional force is acting, and the "work required to stop the car" (sometimes called "the work done by friction") is equivalent to the amount of mechanical energy converted to thermal energy by the action of the car's brakes. The driver of a 800 kg car decides to double the speed from 22.8 m/s to 45.6 m/s. What effect would this have on the amount of work required to stop the car, that is, on the kinetic energy of the car? Give your answers to the following questions in joules. (a) The kinetic energy at a speed of 22.8 m/s would be J (b) The kinetic energy at a speed of 45.6 m/s would be J (c) How many times more work is required to stop the car now that it is going twice as fast? Two times as much work is required, therefore (assuming that the amount of friction force when the brakes are applied is a constant) two times as much distance will be required for the car to stop. Three times as much work is required, therefore (assuming that the amount of friction force when the brakes are applied is a constant) three times as much distance will be required for the car to stop. The same amount of work is required in each case, therefore (assuming that the amount of friction force when the brakes are applied is a constant) the same amount of distance will be required to stop the car when it is moving at twice the speed. Four times as much work is required, therefore (assuming that the amount of friction force when the brakes are applied is a constant) four times as much distance will be required for the car to stop.

Explanation / Answer

Kinetic energy is equal to mass times speed squared multiplied by .5, so...

a.) KE = (.5)(m)(v^2) = (0.5) (800 kg) (22.8^2) = 207936 J

b.) KE= (0.5) (800) (45.6^2) = 831744 J

c)  Four times the work.

Work is energy. All the energy in the question is kinetic.

Kinetic energy is proportional to the square of the difference in velocity.

So, if the car is traveling 2 times faster, the energy (work) required is 2^2 = 4 times as much.

If the car is traveling 3 times faster, the energy (work) required is 3^2 = 9 times as much.

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