Question

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 $7^{th}$ coin (counted from the bottom) due to all the coins on its top,
b) the force on the $7^{th}$ coin by the eighth coin,
c) the reaction of the 6th coin on the $7^{th}$ coin.

Answer 1

a) Force on the seventh coin is exerted by the weight of the three coins on its top.
Weight of one coin = mg
Weight of three coins = 3mg
Hence, the force exerted on the $7^{th}$ coin by the three coins on its top is 3mg. This force acts vertically downward.

b) Force on the seventh coin by the eighth coin is because of the weight of the eighth coin and the other two coins (ninth and tenth) on its top.
Weight of the eighth coin = mg
Weight of the ninth coin = mg
Weight of the tenth coin = mg
Total weight of these three coins = 3mg
Hence, the force exerted on the $7^{th}$ coin by the eighth coin is 3mg. This force acts vertically downward.

c) The 6th coin experiences a downward force because of the weight of the four coins ($7^{th}$, $8^{th}$, $9^{th}$, and ${10}^{th}$ ) on its top. Therefore, the total downward force experienced by the 6th coin is 4mg. As per Newton’s third law of motion, the 6th coin will produce an equal reaction force on the $7^{th}$ coin, but in the opposite direction. Hence, the reaction force of the 6th coin on the $7^{th}$ coin is of magnitude 4mg. This force acts in the upward direction.