Question

A father and his seven year old son are facing each other on ice skates (assume no friction with the ground). With their hands, they push off against one another. Regarding the forces that act on them as a result of this and the accelerations they experience. Which of the following statements is correct?
A. Father exerts more force on the son and experiences less acceleration.
B. Son exerts less force on the father and experiences more acceleration.
C. Father exerts as much force on the son as the son exerts on the father, but the father experiences less acceleration.
D. Father exerts as much force on the son as the son exerts on the father, but the father experiences more acceleration.

Answer 1

Hint: In order to solve this problem we need to use Newton’s third law, it states that every action has an equal and opposite reaction. Doing this will give us information about forces in each other and for acceleration, we need to use Newton’s second law of motion. Doing this will solve your problem and will give you the right answer.

< b>complete step-by-step answer
The situation is a father and his seven year old son are facing each other on ice skates (assume no friction with the ground). With their hands, they push off against one another. It is given that there is no friction so the frictional force will be zero. We need to talk about the forces and accelerations according to the options above.
From Newton's third law that every action has an equal and opposite reaction, we can say that the normal forces exerted by father and son on each other will be equal as the forces make an action-reaction pair.
So, the forces are equal.
And from Newton’s second law of motion that is force is equal to mass times acceleration, we can say that the mass of the father will be more than that of his seven year old son.
So, the acceleration of a son will be more and that of his father will be less.
Let the force exerted on each other be F.
Mass of son and father be ${M_s}$ and ${M_f}$.
We know that ${M_s} < {M_f}$
Their accelerations are ${a_s}$ and ${a_f}$.
So, according to the formula F = Ma, so $a = \dfrac{F}{M}$ so, whose mass is less, his acceleration will be more. We can say that ${a_s} > {a_f}$ since the mass of the son is lesser than that of his father.
So, the acceleration of a father is less than that of his son.
Therefore the correct option is C.

Note: When you get to solve such problems you need to use Newton’s laws of motion. These laws are very important in mechanics and students should know this according to sequence first, second and third law since sometimes it is asked in question like by Newton's second law of motion, so knowing the sequence is very important.