Page:Conservationofen00stew.djvu/106

90 impact it has $$15 \times 17 = 255$$ units, so that its momentum has been increased by 30 units in its previous direction.

The force of impact has therefore generated 30 units of momentum in two opposite directions, so that, taking account of direction, the momentum of the system is the same before and after impact; for before impact we had a momentum of $$10 \times 20 + 15 \times 15 = 425$$, while after it we have the united mass 25 moving with the velocity 17, giving the momentum 425 as before.

125. But while the momentum is the same before and after impact, the visible energy of the moving mass is undoubtedly less after impact than before it. To see this we have only to turn to the expression of Art. 28, from which we find that the energy before impact was as follows:—Energy in kilogrammetres $$= \frac{mv^2}{19.6} = \frac{10 \times 20^2 + 15 \times 15^2}{19.6} = 376$$ nearly; while that after impact $$= \frac{25 \times 17^2}{19.6} = 368$$ nearly.

120. The loss of energy will be still more manifest if we suppose an inelastic body in motion to strike against a similar body at rest. Thus if we have a body of mass 20 and velocity 20 striking against one of equal mass, but at rest, the velocity of the double mass after impact will obviously be only 10; but, as regards energy, that before impact will be $$\frac{20 \times 20^2}{19.6} = \frac{8000}{19.6}$$ while that after