03 Boomerang Ball (2)

03 Boomerang Ball (2)#

Aim#

The concept of impulse explains this very peculiar behavior of a bouncing ball.

Subjects#

  • 1K10 (Dynamic Torque)

  • 1N10 (Impulse and Thrust)

Diagram#

../../../../../_images/figure_040.png

Fig. 97 .#

Equipment#

  • Superball.

  • Table.

Safety#

  • A superball can jump into many unexpected directions, so mind vulnerable objects in the neighborhood.

Presentation#

The table is positioned as shown in Diagram. The ball is thrown as shown. The ball bounces to a fro.

Explanation#

As a basis to explanation see the demonstration Boomerang ball. Using a large basketball thrown against the floor and then bouncing against a vertical wall, shows that after hitting the vertical wall the basketball still rotates clockwise. Figure 98A shows this.

../../../../../_images/figure_130.png

Fig. 98 .#

(The effect of the friction force \(F_{R}\) in \(\mathrm{Q}\) is not that large as that of \(F_{R}\) in \(\mathrm{P}\), since the ball approaches the vertical wall with \(\vec{p}_{h}\) and this momentum is smaller than

\(\vec{p}_{v}\) in P.)

Having hit the vertical wall the ball climbs steep (see Figure 98A). A parabolic trajectory follows. On hitting the floor in \(\mathrm{R}\), the friction force is directed to the right (Figure 98B). The impulse \(\int F_{r} d t\) is large enough to make the component

\(\vec{p}_{h}\) change direction and \(\bar{M}=\vec{r} \times \vec{F}_{R}\) is inducing a counter clockwise rotation. It bounces towards \(\mathrm{S}\) and again \(F_{R}\) is directed to the inner side of the parabola, making the component \(\vec{p}_{h}\) reverse direction and \(\bar{M}=\vec{r} \times \vec{F}_{R}\) inducing clockwise rotation. And so on.

Remarks#

  • Practicing this demonstration against a real wall will learn that this part of the demonstration can also be appreciated on its own. Having the right speed and right angle, a very high climbing ball will be the result of your practicing. Figure 98A shows the explanation of this phenomenon: After bouncing at \(\mathrm{Q}\), \(\vec{p}_{v}\) has a very high value.

  • A nice variation to this demonstration is the “drunken student” (sorry, “drunken sailor”). To throw a ball that follows such a staggering trajectory, see Figure 99.

../../../../../_images/figure_214.png

Fig. 99 .#

Sources#

  • Walker, J., Roundabout, the Physics of Rotation in the Everyday World, pag. 8-12.

  • American Journal of Physics, pag. 875-883 (Vol. 72-7; 2004).

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