# Should the coin be heavier or lighter in the coin drop experiment?

The Coin Drop experiment is a classic experiment used to demonstrate Newton's First Law of Motion. In this experiment, a glass is covered with a card and a coin is place on the card. The card is given a quick strike and the coin falls in the glass. (YouTube Demonstration).

Should the coin be heavier or lighter in this experiment?

The following two statements give contradictory conclusions:

• If the coin is heavier it means it has greater inertia. So it wishes to remain in its state of rest compared to a lighter coin. So, a heavier coin will fall vertically down.

• If the coin is heavier, the normal contact force between it and the card is large compared to that in case of a lighter coin. So, the friction between a heavier coin will and the card will be higher than a lighter coin and the card. So, using a heavier coin will make the coin travel along with the card, instead of falling vertically down.

It can be seen the factors contributing to inertia and friction give contradictory conclusions. So, does the mass of the coin used in the experiment affect the quality of the final result, or it doesn't matter? If mass matters, why is one factor out of inertia and friction is chosen over the other? Or does it depend upon which of the above two factors dominate and vary from one experiment to another, or while using pair of surfaces of different coefficients of friction?

• Try the experiment with coins of different sizes and masses. What do you observe ? Now replace the smooth card with a piece of sandpaper. What do you observe ? – gandalf61 Nov 15 '19 at 16:52

The mass doesn't make a difference. The two competing effects represented by your bullet points cancel each other out, so you will get the same result whether the coin is a heavier or lighter one.

• Could you please explain the reason for that? – Guru Vishnu Nov 15 '19 at 15:31
• Peter covers it in his answer. The frictional force on the coin is mgf. The resulting acceleration of the coin is is given by ma = mgf, so a=gf. That means the acceleration of the coin is independent of its mass. – Marco Ocram Nov 15 '19 at 17:05
• @MarcoOcram The same explanation is used for objects of different mass falling to Earth with the same acceleration. There is a greater accelerating force on objects with more mass, but they also have a greater resistance to acceleration (inertia). The two factors cancel out exactly. – sammy gerbil Jan 25 at 22:42

ma = mgf where f is the coefficient of friction. As you can see the mass of the coin cancels out. So there are 2 things here that you can control. First is the coefficient of friction so the smoother the surfaces the more ideal. 2nd is the acceleration on the card itself so in comparison the acceleration of the coin would be negligible.

What is your purpose in doing this experiment? It shows that objects in motion tend to stay in motion, while objects at rest tend to stay at rest. The quarter demonstrates that by not flying around the room randomly. And also by not missing the cup when a small sideways force is applied.

It sounds like you want to minimize the sideways motion, and you wonder how the weight of the coin matters.

There are a variety of kinds of friction, and the rules for them are different. On average usually the weight more-or-less balances out with the increased friction from the weight, so it won't matter much. Some of the friction comes from deformation of the card's surface, and it is assumed that this will vary linearly with the weight. We kind of assume that the card is a spring. But your card might bend nonlinearly with weight. And of course since the card's friction against the coin and the glass both goes up with coin weight, you will need more force to get the same speed. The slower the speed, the more time that friction is applied to the coin.

If you take it to extremes, weight will matter. If you use a disk of aluminum foil, air resistance etc will become important when it was trivial for heavy weights.

If you want to minimize the sideways motion of your coin, minimize the friction and maximize the force on the card. Perhaps coat the card with powdered graphite, or use a stiff teflon card. Hit the card as hard as you can so it will move fast.