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A box is put on a scale that is adjusted to read zero when the box is empty. A stream of marbles is then poured into the box from a height h above its bottom at a rate of R (marbles per second). Each marble has mass m. The collisions are completely inelastic; assume that the marbles stick to the box without bouncing when they hit. Find the scale reading at time t after the marbles begin to fill the box. Determine a numerical answer when R = 120 s-1, h = 7.80 m, m = 4.50 g, and t = 8.0 s.

Respuesta :

Answer:

[tex]F_{net} = 49 N[/tex]

Explanation:

As we know that rate of marble that strike the target is given as

[tex]R = 120 per s[/tex]

now we know that after t = 8 s total marbles that accumulated in the box is given as

[tex]N = Rt[/tex]

[tex]N = 120(8)[/tex]

[tex]N = 960 [/tex]

now total weight of the marbles is given as

[tex]W = N(mg)[/tex]

[tex]W = 960(4.5 \times 10^{-3})(9.81)[/tex]

[tex]W = 42.37 N[/tex]

Now force due to impact of marble is given as

[tex]F = \frac{dN}{dt}mv[/tex]

[tex]v = \sqrt{2gh}[/tex]

[tex]v = \sqrt{2(9.81)(7.80)} = 12.37 m/s[/tex]

now we have

[tex]F = 120(4.5 \times 10^{-3})(12.37)[/tex]

[tex]F = 6.68 N[/tex]

so total force on the box is given as

[tex]F_{net} = W + F[/tex]

[tex]F_{net} = 42.37 + 6.68[/tex]

[tex]F_{net} = 49 N[/tex]

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