Three forces on a box in different directions what is the acceleration

[Lucaburra]

Homework Statement

Force A 250 degrees @ 200 N
Force B 150 degrees @ 300 N
Force C 50 degrees @ 400 N
mass = 40kg
mew = .14
what is acceleration

Homework Equations

Fa^2 = Fy net^2 x Fx net^2
Fn = Fg
Ff = Fn x mew
Fnet = Fa - Ff
F= ma

The Attempt at a Solution

Fax=Cos 20 (200) = -187.93
Fay = Sin 20 (200) = -68.40

Fbx = Sin 30 (300) = 150
Fby = Cos 30 (300) = -259.81

Fcx = Cos 50 (400) = 257.11
Fcy = Sin 50 (400) = 306.42

Fx net = 219.18 N
Fynet = -21.79 N

Fa^2 = Fxnet^2 + Fynet^2
Fa^2 = 219.18^2 + -21.79^2
Fa^2 = 48039.87 + -474.80
Fa^2 = 47565.07
Fa = 218.09 N

Fn = 9.81 m/s^2 x 40Kg = 392.40N

Ff = Fn (mew) = 392.40N (.14) = 54.94 N

Fnet = Fa - Ff = 218.09 - 54.94 = 163.15 N
a = F/m = 163.15/40 = 4.08 m/s

I'm just not sure I've done this correct

 

[voko]

The components of Fa and Fb are not computed correctly. BTW, you could make your life easier by choosing x to coincide with one of the forces, say Fc, then Fcx = 400 N and Fcy = 0, and the angles of the other forces are relative to Fc, i.e., 200 and 100.

 

[Lucaburra]

Sorry voko I don't follow. I drew my x,y graph and entered the force vectors. I then used the angles relative to the x axis, (as the text says) hence F ax = Cos 20 and F bx = Sin 30. I'm not sure about your meaning to "choose x to coincide with one of the forces." I'm in grade 11 and this is what we were taught to do.

 

[voko]

No problem, you can ignore this part. But the components of Fa and Fb are still not computed properly. For example, Fax = Fa cos 250 = -68.4 N.

 

[Nickie]

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Your calculations and approach seem to be correct. However, it would be helpful to provide a diagram or a clear explanation of the direction of each force and how they are affecting the box. This will help in understanding the final acceleration value and its direction. Additionally, it would be beneficial to include units for the final acceleration value (m/s^2). Overall, your solution appears to be accurate and well thought out.