How Does Angled Force Affect Maximum Box Weight on a Frictional Surface?

[erok81]

Homework Statement

You push down on a box at an angle 15° below the horizontal with a force of 650 N. If the box is on a horizontal surface and the coefficient of static friction is 0.7, what is the heaviest box you will be able to move?

Homework Equations

F=ma

The Attempt at a Solution

So I've solved this problem using Fnet which was 650cos15 for the horizontal force and then subtracted $$(\mu_s)(9.80)(m)$$ The ma part goes to zero since it's not accelerating.

Therefore I get $$650cos15 = (\mu)(9.80)(m)$$ and then solve for m.

I thought that was it. But now that I thinking about it more, there is a vertical component for the force. I'd imagine that extra force would make the box seem to weigh more, thereby increasing friction, making the box weigh less.

Do I factor that vertical force in? If so, how?

 

[erok81]

Ah! Maybe like this?

$$650cos15 = [((\mu)(9.80)(m))+(650sin15)$$

All I did here was add in the vertical force component to the friction.

Yeah...that isn't right since my box ends up weighing 2kg.

 

[Interceptor_1]

Your above equation is correct.Though you will multiply the coefficient of friction to both the weight as well as 650sin15

 

[erok81]

Nice.

So something like this?


$$650cos15 = [((\mu)(9.80)(m))+((\mu)(650sin15))]$$

 

[Interceptor_1]

Yeah,that's correct.

 

[erok81]

Thanks for the help!