Ten one-rupee coins are put on top of each other on a table. Each coin has a mass m. Give the magnitude and direction of (a) the force on the 7th coin (counted from the bottom) due to all the coins on its top, (b) the force on the 7th coin by the eighth coin, (c) the reaction of the 6th coin on the 7th coin.
Given, the mass of each coin is m kg .
(a)
The force that is applied on the 7th coin, which is counted from the bottom, is the weight of three coins that lie above the coin. It can be calculated by subtracting the mass of all the coins with the number of coins below the particular coin.
We know,
Weight = Mass × Acceleration due to gravity = m g
Here, g is the acceleration due to gravity.
The equation to determine the force applied is,
F = Total weight − ( Weight due to 7 coins ) = 10 m ( g ) − 7 m ( g ) = 3 m g N
Thus, the force that acts on the 7th coin is 3 m g N .
(b)
The number of coins above the 8th coin is 2. So the weight of those coins is acting on the eighth coin.
The weight of the eighth coin is also acting on the seventh coin. So the force acting on the 7th coin by the eighth coin is equal to the sum of the weight of the two coins above 8th coin and the 8th coin itself.
The equation to find the force that is acting on the 7th coin is,
F = 2 m ( g ) + m ( g ) = 3 m g N
Thus, force of 3 m g N acts on the 7th coin in the downward direction.
(c)
The reaction of the sixth coin on the 7th coin will be equal to the force applied on it by the upper four coins.
The equation for the reaction force is,
R = − F 4 coins = − 4 m g N
Thus, the reaction of the 6th coin on the 7th coin is 4 m g N .
Given, the mass of each coin is
(a)
The force that is applied on the 7th coin, which is counted from the bottom, is the weight of three coins that lie above the coin. It can be calculated by subtracting the mass of all the coins with the number of coins below the particular coin.
We know,
Here,
The equation to determine the force applied is,
Thus, the force that acts on the 7th coin is
(b)
The number of coins above the 8th coin is 2. So the weight of those coins is acting on the eighth coin.
The weight of the eighth coin is also acting on the seventh coin. So the force acting on the 7th coin by the eighth coin is equal to the sum of the weight of the two coins above 8th coin and the 8th coin itself.
The equation to find the force that is acting on the 7th coin is,
Thus, force of
(c)
The reaction of the sixth coin on the 7th coin will be equal to the force applied on it by the upper four coins.
The equation for the reaction force is,
Thus, the reaction of the 6th coin on the 7th coin is
