Answer :
Constant velocity means that the net force of the system is 0. So the force of friction must equal the horizontal force applied to the box. In other words the force of friction acting on the box is equal to 20 N. Hope that helps.
The force of friction acting on the box will be [tex]\boxed{20\,{\text{N}}}[/tex] acting in backward direction.
Further Explanation:
The force acting on a body in a particular direction results in the acceleration of the object due to that force.
[tex]\boxed{{F_{net}} = m \times a}[/tex]
If the object moves along the path with a constant velocity, then it means that the acceleration of the body is zero. If the acceleration of the body is zero, then there will be no net force acting on the block.
[tex]\begin{aligned}{F_{net}}&=m\times0\\&=0\,{\text{N}}\\\end{aligned}[/tex]
Since here the box is moving on a rough floor and the force applied in the forward direction is [tex]20\,{\text{N}}[/tex]. In order to move with constant velocity, the net force on the block should be zero.
The net force on the block due to applied force and the friction force is:
[tex]{F_{net}}=F-{F_{{\text{friction}}}}[/tex]
Substitute [tex]0\,{\text{N}}[/tex] for [tex]{F_{net}}[/tex] and [tex]20\,{\text{N}}[/tex] for [tex]F[/tex] in above expression:
[tex]\begin{aligned}0&=20-{F_{{\text{friction}}}}\hfill\\{F_{{\text{friction}}}}&=20\,{\text{N}}\hfill\\\end{aligned}[/tex]
Thus, the force of friction acting on the box will be [tex]\boxed{20\,{\text{N}}}[/tex] acting in backward direction.
Learn More:
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Force and Acceleration
Keywords:
Horizontal force, 20 N, 5.0 kg box, rough horizontal floor, constant velocity, magnitude of force, friction acting on box, zero acceleration, no net force.
