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¶

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 2A shows this.

(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 2A). A parabolic trajectory follows. On hitting the floor in $\mathrm{R}$, the friction force is directed to the right (Figure 2B). 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 2A 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 3.

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).