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i cannot work this out can you help please?

i have an mechanical engineering question that i cannot answer:

a car of mass 1400kg is traveling at a velocity of 90km/h. the brakes are applied to the car and its velocity is reduced to rest over a distance of 125m. Determine

a) the loss of kinetic energy

b) the force required at the brakes to stop the car?

help please

3 Answers

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  • RickB
    Lv 7
    6 years ago

    a) Its initial kinetic energy was: ½mv². This is reduced to zero when the car stops; so the loss of KE is ½mv². Convert the velocity from "km/h" to "meters/sec", and this will make the KE number come out in Joules (the standard unit).

    b) change in KE = total work done = force × distance

    You in Part (a) that the change in KE is ½mv², and you know that the distance is 125 meters. Substitute:

    ½mv² = force × 125 meters

    or:

    force = ½mv² / (125 meters)

    Note that this is the force that the ROAD exerted on the wheels of the car. They asked for "the force required at the brakes," which seems to mean the force of your foot on the brake. This is almost certainly NOT the same as the amount of force exerted by the road, and there's no way to determine it without more info. Tell that to your teacher.

  • 6 years ago

    a) kinetic energy is (1/2)mv^2 when it's moving, and 0 when it is stopped.

    b) The work done by the brakes is W = F * d. The work is the same as the loss in kinetic energy, so you have W. And you have d.

  • Steve
    Lv 7
    6 years ago

    V = 90/3.6 = 25 m/s

    a = V²/(2x) = 2.5 m/sec²

    a) KE = ½m*V² = 437500 J

    b) F = m*a = 3500 N

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