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A swift blow with the hand can break a pine board. As the hand hits the board, the kinetic energy of the hand is trans- formed into elastic potential energy of the bending board, if the board bends far enough, it breaks. Applying a force to the center of a particular pine board deflects the center of the board by a distance that increases in proportion to the fore. Ultimately the board breaks at an applied force of 800 N and a deflection of 1.2 cm.
a. To break the board with a blow from the hand, how fast must the hand be moving? Use 0.50 kg for the mass of the hand.
b. If the hand is moving this fast and comes to rest in a dis- tance of 1.2 cm, what is the average force on the hand?

Respuesta :

Cricetus

(a) The velocity is "6.2 m/s".

(b) The average force is "800.83 N".

According to the question,

Force,

  • F = 800 N

Deflection,

  • x = 1.2 cm

           = [tex]1.2\times 10^{-2} \ m[/tex]

As we know,

The work done,

→ [tex]W = F\times d[/tex]

       [tex]= 800\times 1.2\times 10^{-2}[/tex]

       [tex]= 9.6 \ J[/tex]

(a)

Given:

Mass of hand,

  • m = 0.50 kg

Now,

→ [tex]\frac{1}{2} mv^2 = 9.6 \ J[/tex]

         [tex]v = \sqrt{\frac{2\times 9.6}{0.50} }[/tex]

            [tex]= 6.2 \ m/s[/tex]

(b)

→ [tex]v^2 = u^2 +2ax[/tex]

→ [tex]a= \frac{v^2}{2x}[/tex]

     [tex]= \frac{(6.2)^2}{2\times 1.2\times 10^{-2}}[/tex]

     [tex]= 1601.67 \ m/s^2[/tex]

hence,

The average force will be:

→ [tex]F_{avg} = m\times a[/tex]

           [tex]= 0.50\times 1601.67[/tex]

           [tex]= 800.83 \ N[/tex]

Thus the above answers are correct.

Learn more:

https://brainly.com/question/23115729

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