Box dragged along floor at an angle, calculating normal and frictional force

[revere21]

Homework Statement

A 60 kg box is dragged along a rough but level floor by a rope at a 30^o angle to the horizontal. The tension in the rope is 150 N, and the box is speeding up at 0.80 m/s² (along the floor).

(a) How large is the frictional force of the floor on the box?

Homework Equations

F_frict = u_k*F_N
F_N = m*g - F*sin(theta)

The Attempt at a Solution

I used F_N = m*g - F*sin(theta) to calculate the normal force, which is needed because it is a component of the equation to find frictional force. So, F_N = (60)(9.8) - (150)sin30 => F_N = 588 - 75 = 513
From here, I know that F_frict = u_k*F_N, but the only thing I can plug in is 513 for F_N, which still leaves me with two unknowns.

Can anyone be so kind as to tell me the next step? Am I missing something? Looking at the problem completely wrong?

 

[SammyS]

What is the horizontal component of the 150 N force?

Then find the net horizontal force. That is equal to ma, which you can get from what you're given.

They don't give you μ_k, but you don't need it. You don't even need the normal force, although you got that just fine.

 

[revere21]

What is the horizontal component of the 150 N force?

Then find the net horizontal force. That is equal to ma, which you can get from what you're given.

They don't give you μ_k, but you don't need it. You don't even need the normal force, although you got that just fine.

The horizontal component would be 129.9 N, I believe. From using cos30 = adjacent/150.

As far as a net horizontal force, where does this come from? Is it just F_horizontal = 60*0.80 = 48?

 

[SammyS]

The horizontal component would be 129.9 N, I believe. From using cos30 = adjacent/150.

As far as a net horizontal force, where does this come from? Is it just F_horizontal = 60*0.80 = 48?

Yes, 48 Newtons.

 

[revere21]

Yes, 48 Newtons.

So, I take the horizontal component of 129.9 N, and the net horizontal force of 48 N, and plug it into F - f = ma? Is that right? That would give me 129.9 - f = 48, which comes out to f = 81.9 N.

Can you give me one final hint and tell me if that is the right way to finish out this problem?

 

[SammyS]

Yes, that's right.

 

[revere21]

Yes, that's right.

Awesome. Thank you, yet again. You, sir, are a freshman-level physics wizard.