Answer:
Friction between the box and the floor is 25N to the left
Step-by-step explanation:
There are two forces acting on the box along the horizontal direction:
- The force of push applied by the worker, in the forward direction, F
- The force of friction,
, acting in the opposite direction (backward)
So the net force acting on the box is
![F_(net)=F-F_f](https://img.qammunity.org/2021/formulas/physics/middle-school/6obxmw2pkeh4zos9ye2ykw6hjf0k0ci9oz.png)
According to Newton's second law of motion, the net force on an object is equal to the product between its mass (m) and its acceleration (a), so we can write:
![F_(net)=ma](https://img.qammunity.org/2021/formulas/physics/high-school/11irvb99rpiabbu2yxl1ix9zxa83cv93dm.png)
And so
![F-F_f = ma](https://img.qammunity.org/2021/formulas/physics/middle-school/559luz4trvtqj3wbsfhnytgrp7gi57daqw.png)
However, in this case the box is moving at constant speed; this means that its acceleration is zero:
![a=0](https://img.qammunity.org/2021/formulas/mathematics/middle-school/qojj0q9t3z4frkq4inqwmhw4kijgvf6s8c.png)
Therefore we have:
![F-F_f=0](https://img.qammunity.org/2021/formulas/physics/middle-school/6b8qc582ugzup5n8w6uji1420mk0jtjlli.png)
Which means
![F_f=F](https://img.qammunity.org/2021/formulas/physics/middle-school/t9dqml1jzrz3zroggbrgt28v58m1r5p96p.png)
And since we are told that
![F=25 N](https://img.qammunity.org/2021/formulas/physics/middle-school/wnar1yaq195idc50s44y2uz3zefptaz98p.png)
This means that the force of friction is also 25 N:
![F_f=F=25 N](https://img.qammunity.org/2021/formulas/physics/middle-school/7u04g2ug2tsnlnxmc7hqi1heqnvxlsz1nr.png)