A Trick with Coin and Playing Card

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A Trick with Coin and Playing Card
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• Turn one of your hands so it is palm up. Form a
  fist but extend your forefinger.
• Balance the playing card on the tip of your
  finger. Place the coin in the centre of the card
  so the card and coin balance.
• Try to remove the card without touching the coin.
  Eventually the coin should still stay balanced on
  the tip of your finger.

3
Should the card be removed slowly or quickly ?
4
Should the card be removed slowly or quickly ?
The trick can be done by flicking the card using
your other hand. Make sure your flick is level
with the card and is not flicking it up or down.
5
Explain why the card flies away while the coin
stays on the finger tip ?
6
Model Answer
The coin stays at rest due to inertia. It is
originally at rest and does not want to change.
Challenge
It is observed that the coin keeps pace with the
card if the card is moved slowly. Why in this
case inertia does not come into play ?
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Analysis of force and motion of the coin in case
it keeps pace with the card.
coin
t 0
card
The card is moved slowly.
3 cm
t 1 s
3 cm
Suppose the coin and the card are displaced by 3
cm from rest in 1 s. Assume they move with
uniform acceleration a. Find a.
8
Analysis of force and motion of the coin in case
it keeps pace with the card.
coin
t 0
card
The card is moved slowly.
3 cm
t 1 s
3 cm
S ut 0.5at2 with S 0.03 m , u 0 and
t 1 s a 0.06 m s-2
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Analysis of force and motion of the coin in case
it keeps pace with the card.
coin
t 0
card
The card is moved slowly.
3 cm
t 1 s
3 cm
What is the force responsible for the
acceleration of the coin ? If the mass of the
coin is 0.007 kg , find the magnitude of the
force.
10
Analysis of force and motion of the coin in case
it keeps pace with the card.
Acceleration a 0.06 m s-2
Mass m 0.007 kg
Friction F
The friction exerted by the card on the coin is
responsible for accelerating the coin forward.
Given the maximum friction is 0.014 N. The
friction required is much smaller than the
maximum friction possible between the coin and
the card. The coin therefore can keep pace with
the card.
F ma 0.007 x 0.06 0.00042 N
11
Analysis of force and motion of the coin in case
it keeps pace with the card.
coin
t 0
card
The card is moved rapidly.
3 cm
t 0.05 s
3 cm
Suppose the coin and the card are displaced by 3
cm from rest in 0.05 s. In this case, the card
is accelerated from rest rapidly, how large the
friction is required in order to keep the coin
pace with the card ?
12
Analysis of force and motion of the coin in case
it keeps pace with the card.
coin
t 0
card
The card is moved rapidly.
3 cm
t 0.05 s
3 cm
S ut 0.5at2 with S 0.03 m , u 0 and
t 0.05 s a 24 m s-2
13
Analysis of force and motion of the coin in case
it keeps pace with the card.
Acceleration a 24 m s-2
Mass m 0.007 kg
Friction F
The friction exerted by the card on the coin is
responsible for accelerating the coin forward.
Given the maximum friction possible between the
coin and the card is 0.014 N. The friction
required to keep the coin pace with the card is
much larger than this. The coin therefore cannot
keep pace with the card.
F ma 0.007 x 24 0.168 N
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The coin cannot keep pace with the card. The
friction acting on it attains its maximum
possible magnitude of 0.014 N.
Acceleration a
Mass m 0.007 kg
Friction F 0.014 N
Find the acceleration of the coin.
F ma 0.014 0.007 a a 2 m s-2
15
The coin cannot keep pace with the card. While
the card is displaced by 3 cm in 0.05 s , the
coin is displaced by S.
coin
t 0
card
S
t 0.05 s
3 cm
S ut 0.5at2 with u 0 , a 2 m s-2
and t 0.05 s S 0.0025 m
Thus the coin only moves by 2.5 mm while the card
moves by 3 cm. Apparently the coin remains at its
original location after the card moves far away.
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Summary

• While the card is being moved, there is friction
  between the coin and the card.
• The friction on the coin is the unbalanced force
  responsible for accelerating it forward. Due to
  the inertia (measured by the mass) of the coin, a
  more rapid change in velocity requires a larger
  unbalanced force on the coin.
• If the card is moved slowly, the coin can keep
  pace with it. This is because the acceleration of
  the coin is small and hence only a small friction
  is required.
• There is an upper limit for the friction between
  the card and the coin.
• If the card is being moved rapidly, the coin
  cannot keep pace with it because the friction is
  not large enough to provide the necessary
  acceleration. The coin only moves slightly under
  the action of the limited amount of friction.

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Go Home
Try using different materials such as sandpaper
or thin plastic, try polishing the card. When is
it harder or easier to flick the card without
disturbing the coin? Try with coins of different
masses. Try again with a stack of coins.
18
Tablecloth yank
Can you pull away the tablecloth from a table and
leave the settings undisturbed?
Is it easier to do when the bottle is full or
empty? Why?
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There is no measurement taken in this experiment
to confirm statements I and II.