08 No Tipping Allowed

Aim

To show that a cylinder that slides to a stop tips only if its diameter-to-height ratio is less than the reciprocal of the coefficient of kinetic friction.

Subjects

• 1K20 (Friction)

Diagram

Fig. 116 .

Equipment

• 5 pvc cylinders, \(\varnothing= 80 \mathrm{~mm}\)

  • \(l_{1}=285 \mathrm{~mm}\)

  • \(l_{2}=320 \mathrm{~mm}\)

  • \(l=335 \mathrm{~mm}\)

  • \(l_{4}=350 \mathrm{~mm}\)

  • \(l=385 \mathrm{~mm}\)

• Horizontal surface (smooth table)

Presentation

The lateral standing cylinder is given a push by hand. (Push the cylinder on the bottom half, a number of times from left to right and vice versa).

Cylinder \(l_{1}\) never tips, \(l_{5}\) always tips, \(l_{2}, l_{3}\) and \(l_{4}\) tip sometimes/often ( \(l_{3}\) tips roughly \(50 \%\) of the times).

Explanation

On the verge of tipping, the upward normal force acts at the leading edge of the base (Figure 117, point A).

Fig. 117 .

In the decelerating reference frame ma acts on the center of mass, along with the vertical gravitational force mg. (See Figure 118).

Fig. 118 .

When the resultant of \(ma\) and \(mg\) is directed to point \(\mathrm{A}\), the cylinder is on the verge of tipping. Figure 118 shows that in that case \(\mu_{k}=d / h\).

Remarks

When constructing the demonstration, you need to know the value of \(\mu_{k}\) before you can cut the cylinder to the proper heights. \(\mu_{k}\) can easily be determined by placing a short cylinder on an inclined board and finding the angle of incline for which the cylinder slides at constant speed after being given an initial push. \(\mu_{k}=\tan (\alpha)\) ( \(\alpha=\) angle of incline).

Sources

• Ehrlich, Robert, Turning the World Inside Out and 174 Other Simple Physics Demonstrations, pag. 43

• Friedrich, Artur, Handbuch der experimentellen Schulphysik, part 2, Mechanik der festen Körper, pag. 128