Question

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.

Answer 1

Answer:

$F_{net} = 49 N$

Explanation:

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

$R = 120 per s$

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

$N = Rt$

$N = 120(8)$

$N = 960$

now total weight of the marbles is given as

$W = N(mg)$

$W = 960(4.5 \times 10^{-3})(9.81)$

$W = 42.37 N$

Now force due to impact of marble is given as

$F = \frac{dN}{dt}mv$

$v = \sqrt{2gh}$

$v = \sqrt{2(9.81)(7.80)} = 12.37 m/s$

now we have

$F = 120(4.5 \times 10^{-3})(12.37)$

$F = 6.68 N$

so total force on the box is given as

$F_{net} = W + F$

$F_{net} = 42.37 + 6.68$

$F_{net} = 49 N$