a bottle is given a push along a frictionless tabletop and slides off the edge of the table (a) what forced are exerted on the bottle while (i) it is being pushed (ii) on the table free of push(iii)falling from the table to the floor. (b) what is the reaction force to each force in part a
To understand the forces exerted on the bottle during different scenarios, let's break down the question into parts.
(a) Forces exerted on the bottle:
(i) While being pushed:
When the bottle is being pushed along the tabletop, there are two forces acting on it. The first force is the pushing force exerted by the person pushing the bottle. This force is directed towards the edge of the table. The second force is the reaction force that arises due to Newton's third law of motion, which states that every action has an equal and opposite reaction. Therefore, the bottle exerts an equal and opposite force on the person's hand.
(ii) On the table free of push:
Once the bottle slides off the edge of the table, it is no longer being pushed. At this point, the only force acting on the bottle is the force of gravity. Gravity pulls the bottle downward towards the floor. Since there is no friction on the tabletop (as mentioned in the question), there are no other opposing forces.
(iii) Falling from the table to the floor:
When the bottle is falling from the table to the floor, the only force acting on it is the force of gravity pulling it towards the ground. Similarly to the previous scenario, there are no opposing forces.
(b) Reaction force to each force in part a:
For every force mentioned in part a, there is a corresponding reaction force:
(i) The reaction force to the pushing force exerted on the bottle is the force that the bottle exerts back on the person's hand.
(ii) As mentioned, when the bottle is on the table free of push, the only force acting on it is gravity. The reaction force to gravity is the normal force exerted by the table on the bottle. The normal force acts perpendicular to the surface of the table and balances out the gravitational force.
(iii) While falling from the table, the reaction force to the force of gravity is the force of the floor pushing back on the bottle. This force is also known as the normal force and balances out the gravitational force.
Remember, understanding the concept of Newton's laws of motion and the nature of forces involved allows you to determine the forces and their reactions in different scenarios.