A box rests motionless on the ground. One student is pushing the box to the right with a force of 25 newtons. The other student is pushing to the left with a force of 50 newtons. In which direction and with what type of speed will the box move?
The box will move according to the second Newton's Law:
`vecF = mveca` , where `vecF` is the net force acting on the box, m is the mass of the box and `veca` is the acceleration.
The net force on the box here is the vector sum of two forces: force 1 of 25 N to the right and force 2 of 50 N to the left.
`vecF = vecF_1 + vecF_2`
Since the forces are along the same line (horizontal), but in opposite directions, the magnitude of the net force will equal the difference of the magnitude of the forces. The direction of the net force will be the same as that of the force with the larger magnitude, that is, to the left.
`F = F_2 - F_1 = 50 N - 25 N = 25 N`
Since the net force is to the left, the acceleration, according to the second Newton's Law, will also be to the left. If the box is initially motionless, its initial velocity is zero, and it will acquire velocity that will depend on time as
`vecv = veca*t` ,
which means that the box will start moving in the direction of the acceleration: to the left. Its speed will increase, because its velocity and acceleration are in the same direction.
The box will move to the left with increasing speed.