Answer:
[tex]m = 44~Kg[/tex]
Explanation:
Net Force
Newton's second law explains the dynamics principles when a number of forces are applied to an object.
The net force vector is the sum of the individual vector forces applied. The magnitude of the net force is related to the magnitude of the acceleration of the body as follows:
[tex]Fn=m.a[/tex]
Furthermore, the acceleration can be calculated if we know the kinematic behavior of the body:
[tex]\displaystyle a=\frac{v_f-v_o}{t}[/tex]
Where vf, vo, and t are the final speed, initial speed, and time, respectively.
The box is pushed across the floor with a force of 25 N against a frictional force of 14 N.
The net force applied to the box is:
[tex]Fn = 25 N - 14 N = 11 N[/tex]
We also know the box is accelerated from rest (vo=0) to vf=4 m/s in t=16 seconds, thus:
[tex]\displaystyle a=\frac{4-0}{16}[/tex]
[tex]a = 0.25~m/s^2[/tex]
From the equation:
[tex]Fn=m.a[/tex]
We solve for m:
[tex]\displaystyle m=\frac{Fn}{a}=\frac{11~N}{0.25~m/s^2}[/tex]
[tex]\mathbf{m = 44~Kg}[/tex]
