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Newton's Third Law - Weight on Scale when catching a ball

  1. Jun 24, 2008 #1
    1. The problem statement, all variables and given/known data

    You are standing on scales which read weight in Newtons. A 0.50 kg ball is dropped from a height of 1 m into your hands. Your hands drop from chest level to waist level during the catch, a distance of about 25 cm. Your mass is 62 kg. Assuming that you decelerate the ball uniformly during the catch, what would be the maximum reading on the scales? (Hint: The scales read 607.6 N before you caught the ball.)

    Weight of person = 607.6N
    Mass of Ball= 0.50 kg
    Displacement of ball when dropped = 1.0 metres
    Displacement of ball during deceleration = 0.25 metres

    2. Relevant equations

    Force = Mass * acceleration

    Force (weight) = Mass * 9.81

    Velocity (final) ^2= Velocity (initial) ^2 + 2 * acceleration * displacement

    Vf^2 = Vi^2 + (2 * a * d)


    3. The attempt at a solution

    Calculate final velocity of ball after it is first dropped before it is caught:


    Vf= x
    Vi= 0 m/s
    a= 9.81 m/s^2
    d= 1.0 metres

    Vf^2 = Vi^2 + (2 * a * d)
    x^2 = 0^2 + (2*9.81*1)
    x^2 = 19.62
    x = 4.43 m/s

    Calculate acceleration (negative) of ball as it is being caught:

    Vf= 0 m/s
    Vi= 4.43 m/s
    a= x
    d= 0.25 metres

    Vf^2 = Vi^2 + (2 * a * d)
    0^2 = 4.43^2 + (2 * x * 0.25)
    0 = 19.62 + (0.50x)
    -0.50x = 19.62
    x = 39.24

    Therefore, the acceleration of the ball as it is being caught is 39.24 metres per second squared downward.


    Now, calculate the force of the ball:

    F=ma
    F=0.5 x 39.24
    F=19.62

    Now, calculate the maximum weight reading on the scale (which occurs as the ball is being caught):

    Weight of man + weight of ball + force of ball during deceleration

    607.6 newtons + (0.5)*(9.81) + 19.62 newtons
    which is...
    607.6 newtons + 4.905 newtons + 19.62 newtons=632.125 newtons

    Thus, the maximum scale reading would be 632.125 newtons.



    Am i right?
     
  2. jcsd
  3. Jun 24, 2008 #2
    Your methodology is right, yeah. Lemme check the math.

    Edit: Yep, you're right.
     
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