# B Penny on a card experiment.... explanation

#### esha

A card kept on a glass with a penny is jerked. The coin falls in the glass while the card moves away. why is that?
My attempt at an explanation
A force acts on the card which is greater than the static friction acting between the card and the coin. Hence the coin is able to overcome that. As the cardboard slips under it a relative motion occurs which is resisted by the kinetic friction. Since the coin has no other force acting in that direction it moves in the direction of the kinetic friction. So the coin falls back in the glass. Am i correct?
My doubts
1) If this is the case then why do we tend to use a heavier coin? If we do so then the coin would cause more static friction which can make the cardboard and the coin fly off together. This wud result into the coin not falling in the glass.

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#### Orodruin

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A force acts on the card which is greater than the static friction acting between the card and the coin.
It does not have much to do with the force on the card. What is relevant is the force on the coin and its size relative to its mass.

Hence the coin is able to overcome that.
There is nothing to overcome. The only force on the coin is the friction (in the horizontal direction). This force will accelerate the coin. The only question is how much it will accelerate the coin. If it is not enough, the coin will fall into the glass.

Since the coin has no other force acting in that direction it moves in the direction of the kinetic friction. So the coin falls back in the glass.
The coin accelerates in the direction the card is being pulled in. If this acceleration is not sufficient, the coin falls into the glass. Note that the coin falling in the glass is a result of the coin not moving enough in the horizontal direction to avoid it.

If this is the case then why do we tend to use a heavier coin? If we do so then the coin would cause more static friction which can make the cardboard and the coin fly off together. This wud result into the coin not falling in the glass.
It will transpire much the same. The frictional force will increase with the mass, but the acceleration is inversely proportional to the mass so it will essentially stay the same.

#### esha

1)by overcoming I mean to say that it needs to overcome the static friction which exists in between any two non smooth surfaces.
2) Its the frictional force causing the acceleration . If we increase the weight the frictional force will increase. This means the acceleration on the coin would too because there is no other force acting on it. Wouldnt that happen?

#### Orodruin

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1)by overcoming I mean to say that it needs to overcome the static friction which exists in between any two non smooth surfaces.
There is nothing to "overcome". Unless you want to go to a reference frame that moves with the card, but that is definitely not advisable at B level. I suggest you just consider the situation in the inertial frame of the glass.

If we increase the weight the frictional force will increase. This means the acceleration on the coin would too because there is no other force acting on it. Wouldnt that happen?
No. As I told you, according to Newton's second law, F = ma, a larger mass requires a larger force. This exactly balances the fact that the frictional force increases.

#### esha

I am considering an non inertial frame of reference of the card.
We are doing problems taking in consideration pseudo forces.
I too agree that the frictional force increases. Doesnt that mean that the acceleration of the coin is increasing?

#### jbriggs444

Homework Helper
The acceleration of the coin from kinetic friction is fixed. What is not fixed is the duration of the interval over which kinetic friction can act. The faster the card slides out from under the coin, the shorter that interval will be. The larger the acceleration on the card, the faster it will slide. The larger the force on the card, the faster it will accelerate.

Push hard enough and the card slides out before the coin can move appreciably.

#### sophiecentaur

Gold Member
The acceleration of the coin from kinetic friction is fixed. What is not fixed is the duration of the interval over which kinetic friction can act. The faster the card slides out from under the coin, the shorter that interval will be. The larger the acceleration on the card, the faster it will slide. The larger the force on the card, the faster it will accelerate.

Push hard enough and the card slides out before the coin can move appreciably.
Good explanation. The only thing missing is the term 'Impulse', of which I am a great fan.
Impulse = Force X time = change of momentum (of the coin)
Even if the coin were 'quite sticky', keep the contact time short enough and the coin would still not experience a big enough change in velocity.

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#### esha

i get it... now.. But I dont understand still why a heavier coin would be better?

#### Nidum

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Do the Physics . Can you draw a free body diagram for the coin ?

#### Orodruin

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i get it... now.. But I dont understand still why a heavier coin would be better?
A heavier coin will not be "better", as has been stated many times already. The reason is essentially the same as the reason things accelerate with the same acceleration in a gravitational field. More force, yes, but this is counterbalanced by more inertia and results in the same acceleration.

#### jimkris69

Everybody is assuming the card has only a horizontal motion but when a card is jerked by a human being there is also created a small amount of vertical motion which will toss the coin off the card thereby reducing the static friction to a very low value.

#### Mister T

Gold Member
i get it... now.. But I dont understand still why a heavier coin would be better?
We're assuming the friction force is proportional to the weight of the coin. It may that that condition is not satisfied. It usually isn't, except in textbook problems.

#### sophiecentaur

Gold Member
except in textbook problems.
This is the problem. People look in text books and try to extend those simple models to real life.
The branch of Physics that sticks best to 'the rules' is electronics circuit work at audio frequencies and below. Take a component out of the drawer and it will probably do exactly what is marked on the side, which is more than can be said for a motor car, aeroplane or boat. You can do the sums and connect it all up and wahddyaknow, the meters say what you expected.

"Penny on a card experiment.... explanation"

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