A large cardboard box of mass 0.75 kg is pushed across a horizontal floor by a force of 4.5 N. The motion of the box is opposed by (i) a frictional force of 1.5 N between the box and the floor, and (ii) an air resistance force kv2, where k = 6 * 10-2 kg m-1 and v is the speed of the box in m s-1.
Sketch a diagram showing the directions of the forces which act on the moving box. Calculate maximum values for (a) the acceleration of the box, (b) its speed.
Answers: (a) 4.0 m s-2, (b) 7.1 m s-1
2. The attempt at a solution
While I do get the correct answers, I am a bit confused.
(a) F = ma
4.5 - 1.5 = 0.75 * a
a = 4 m s-2
(b) 4.5 = 1.5 + kv2
3 = 6 * 10-2 * v2
v = 7.1 m s-1
My confusion is the following: if 4.5 N which is moving "forward" equals to 1.5 N and the air resistance force kv2 how does the box actually move? Shouldn't it stand still? I known that a body might be in equilibrium and can move (e. g. a brick on a rope spun in a circle) but not sure how to apply it to this situation (whether this applies at all). And if it is equal, then why not 4.5 - 1.5 - kv2 = 0.75 * a?
Maybe my graph is wrong and that is why I don't see the situation in the right way. Or maybe my calculations are wrong and I luckily got a similar answer.
Thanks in advance for any help!