College

Nina and Jon are practicing an ice skating routine. Nina is standing still. Jon, who is twice as heavy as Nina, skates toward her, pushing Nina away with force [tex]$f$[/tex]. Assuming the system is closed, which statement is correct about this system?

A. Nina experiences a force equal to [tex]$2f$[/tex].

B. Nina experiences a force equal to [tex]$f^2$[/tex].

C. Nina experiences a force equal to [tex]$f$[/tex].

D. Nina experiences a force equal to [tex]$\frac{f}{2}$[/tex].

Answer :

The question involves a closed system where Nina and Jon are interacting through the application of force. Let's go through the reasoning step-by-step:

1. Understand the Problem: Nina is standing still while Jon exerts a force [tex]\( f \)[/tex] on her as he skates toward her. Jon is said to be twice as heavy as Nina. We want to determine the force that Nina experiences.

2. Physical Principles: In a closed system involving two people exerting forces on each other, according to Newton's Third Law of Motion, every action has an equal and opposite reaction. This implies that when Jon pushes on Nina with a force [tex]\( f \)[/tex], Nina will also exert an equal force back on Jon.

3. Application of Newton's Third Law: It doesn't matter that Jon is twice as heavy; the force experienced by Nina will be equal to the force applied on her. The law states that the forces between the two people are equal in magnitude and opposite in direction.

4. Conclusion: Therefore, Nina experiences a force equal to [tex]\( f \)[/tex].

So, the correct statement is: Nina experiences a force equal to [tex]\( f \)[/tex].