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March 26, 2017

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hey im not good with story problems the question is david purley, survived decceration from 173km/h to 0 km/h over a distance of .660 m when his car crashed. Assume that Purley's mass is 70.0kg. What is the mgnitude of the average force acting on him during the crash? Compare the force to Purley's weight.

  • Science - ,

    You need to calculate the average force. For this, we use Newton's second law, which states that:

    F = m*a (where F stand for force, m is mass and a is acceleration).

    Since the mass of the person was already given, we only need to calculate the persons acceleration.

    One of the equations used in kinematics (science of motion) is the following:

    v^2 = vo^2 - 2*a*x
    (where v is the final speed in meters/s, vo the initial speed in meters/s, a the acceleration, and x the distance travelled in meters)

    So, if we rewrite this formula, we find that: a= (vo^2 - v^2)/(2*x)

    173 km/h = 48 m/s

    so: a = (48^2 m²/s²- 0)/(2*0.660 m) = 1745.45 m/s²

    Now, since Purley's mass is 70.0 kg, we find that:

    F = m*a = 70.0 kg * 1745.45 m/s² = 122181,82 N = 122.18 kN

    So the average force exerted on Purley's body equals 122.18 kN.

    With the same formula, we can find Purley's weight (when we replace a with the gravitational acceleration g).

    F = m*g = 70.0 kg * 10 m/s² = 700 N

    So Purley's weight is only 700N. This means that the force acting on him during the crash is about 175 times that of his own weight.

    This explains why people often experience serious bone fractures or internal injuries during a car crash. The average force acting on them is certainly large enough to break some bones.

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