Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

Here's my problem and the work I've done. The time is already past for me to submit the answer, but I want to know where I went wrong and why I was wrong.

The 2-kg box slides down a vertical wall while you push on it at a 45 degree angle from below. Both the box and the wall are wood. What magnitude of force should you apply to cause the box to slide down at a constant speed?

The coefficient of kinetic friction for wood-wood is 0.2.

The vertical forces acting on the box are:

$F_{box}$(sin 45) - $F_{friction} - mg$ = 0

where

$F_{box}$ = force acting on the box

$F_{friction}$ = frictional force opposing the motion

$m$ = mass of the box

$g$ = acceleration due to gravity

Hence

$F_{friction} = F_{box}$(sin 45) - $mg$ --- call this Equation 1

The normal force acting on the box is as follows:

$F_{box}$(cos 45) = $F_n$

and since

$F_{friction}$ = µ$F_n$, then

$F_{friction}$ = µ($F_{box}$)cos 45 --- call this Equation 2

Setting Equation 1 = Equation 2,

$F_{box}$(cos 45) - $mg$ = µ($F_{box}$)cos 45

Simplifying the above for "$F_{box}$"

$F_{box}$(cos 45) - $F_{box}$(µ*cos 45) = $mg$

$F_{box}$(sin 45 - µcos 45) = $mg$

and solving for "$F_{box}$"

$F_{box}$ = $\frac{mg}{cos 45 - µcos 45}$

Substituting appropriate values and calculating for "$F_{box}$"

$F_{box}$ = 34.65N

The system says that the solution is 23N. How did they get that and where is my mistake?

share|improve this question

1 Answer 1

up vote 2 down vote accepted

The box is sliding vertically down at constant speed after overcoming your force F and friction, so the equation of forces in vertical direction should be

$mg = F_{box}(sin 45) + F_{friction} $

Repeat your calculation with the above equation, then you will get the correct answer.

share|improve this answer
    
Damn, I looked at the problem and made the same mistake as Tyler :-) –  John Rennie Oct 3 '13 at 7:01
    
thanks a lot. I wouldn't have seen that otherwise. I appreciate it. –  Tyler Murphy Oct 4 '13 at 2:54

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.