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 ${6^{th}}$coin on the ${7^{th}}$ coin.

Answer 1

We will use here the formula of force exerted by a body due to its weight, $F = mg$. Weight of one coin is $mg$ then weight of two coin is $2 \times$weight f one coin. Weight always exerts force vertically downwards and reaction force to weight always exerts force vertically upwards.

Complete step by step answer:
a) Force on seventh coin count from bottom is force exerted by the weight of three coins over it. Weight of one coin is $mg$N. So the weight of three coins will be $3mg$N.
Hence, the force exerted on the seventh coin counted from the bottom is $3mg$N.
Here, Direction of force will be vertically downwards in the direction of weight of the coins.

b) The eighth coin is already under the weight of two coins above it and it has its own weight too. Hence the force on the seventh coin due to the eighth coin is the same as the force exerted on the seventh coin by three coins. Therefore, the force on the seventh coin by eight coin will be $3mg$N. Here, direction of force will be vertically downwards in the direction of weight of the coins.
c) The sixth coin is under the weight of four coins above it. Therefore, the sixth coin experiences a downward force because of four coins over it. So, the weight of four coins will be $4mg$N. Hence, the force exerted by the sixth coin on the seventh coin will be $4mg$N.
Here, direction of force will be vertically upwards as the sixth coin exerts a reaction force against the force of four coins weight vertically.
We can also write the force exerted by the sixth coin on the seventh coin is $- 4mg$N. Since minus shows the opposite direction of reaction force from the force of weight.

Note: Remember that minus sign denotes the direction of the force on the body. Force cannot be exerted in minus value. Magnitude of Force will be always positive. Also while solving such problems use equilibrium(Newton’s second law) and action-reaction(Newton’s third law) on different systems as required to reach the final solution.