Basic Force: Why to take force of friction from force applied y?

[Arooj]

Homework Statement

A box of books weighing 319 N is shoved across the floor by a force of 485 N exerted downward at an angle of 35^degrees below the horizontal.

a) If uk between the box and the floor is 0.57, how long does it take to move the box 4.00 m, starting from rest.

b) If uk between the box and the floor is 0.75, how long does it take to move the box 4.00 m, starting from rest?

Homework Equations

Just for this problem: Ff = (FsinΘ+W)µ (F=485)
Fnet = FcosΘ - Ff

The Attempt at a Solution

I understand how to do this problem, but why is it that you take the force of friction from the y component of the force rather than the x component of the force?

 

[azizlwl]

Homework Statement

A box of books weighing 319 N is shoved across the floor by a force of 485 N exerted downward at an angle of 35^degrees below the horizontal.

a) If uk between the box and the floor is 0.57, how long does it take to move the box 4.00 m, starting from rest.

b) If uk between the box and the floor is 0.75, how long does it take to move the box 4.00 m, starting from rest?

Homework Equations

Just for this problem: Ff = (FsinΘ+W)µ (F=485)
Fnet = FcosΘ - Ff

The Attempt at a Solution

I understand how to do this problem, but why is it that you take the force of friction from the y component of the force rather than the x component of the force?

Ff=Nμ
Find the value of N.

 

[Arooj]

N = FsinΘ + W
N = 485(sin35) + 319
N = 597.2

 

[azizlwl]

The friction is depend on normal force which is in y direction.
The frictional force is perpendicular to normal force and it opposes the motion.

 

[Nickie]

The force of friction is a component of the net force acting on the object, which determines its motion. In this case, the force of friction acts in the opposite direction of the applied force, so it must be subtracted from the applied force to find the net force. Since the force of friction acts along the surface of contact (in the y direction), it must be subtracted from the y component of the applied force in order to find the net force in the y direction. This net force, along with the x component of the applied force, can then be used to calculate the acceleration and ultimately, the time it takes for the box to move a certain distance. This is a fundamental concept in Newton's second law, which states that the net force on an object is equal to its mass times its acceleration.