Newton's third law we find that the correct statement for the forces that push the pencil on the table is:
c) Normal friction
Newton's third law establishes that the force acts in pairs one of them is called action and the other reaction, one on each interacting body, the two are of the same magnitude and of opposite direction.
In the attached diagram we have a free-body diagram of the force on the pencil on the table. Let's analyze the statements to find the force that pushes the pencil up.
a) False. Gravity is directed towards the center of the earth, therefore it acts downwards.
b) False. Friction is the one that opposes the displacement of the pencil tip is horizontally.
c) True. The Normal Force is the reaction of the Earth by the support of the pencil on the surface, acts in a vertical direction upwards.
d) False. The sliding friction in the friction force that is put to the displacement of the entire pencil, is in the horizontal direction.
In conclusion using Newton's third law we find that the correct statement is:
c) Normal friction
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