- #1

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## Homework Statement

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

*kv*

^{2}, 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 + kv

^{2}

3 = 6 * 10

^{-2}* v

^{2}

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 kv

^{2}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 - kv

^{2}= 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!