Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 200 N and b = 400 N. Round y
our answers to one decimal place.)
1 answer:
Answer: R = 346.4N and angle 30° to the horizontal negative axis
Explanation:
To find the resultant force, we need to sum up the forces on the vertical and horizontal axis.
For the horizontal axis;
Rx = -b + acos60
Rx = -400N +200cos60
Rx = -400N +100N
Rx = -300N
For the vertical axis;
Ry = asin60 = 200sin60
Ry = 173.2N
The resultant force R can be given as;
R = √(Rx^2 +Ry^2)
R = √((-300)^2 + 173.2^2)
R = 346.4N
Angle z can be written as
Tanz = Ry/Rx
z = taninverse (Ry/Rx)
z = taninverse (173.2/300)
z = 30°
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R3 and R4 are in series so
Rtotal= R3+R4 = 6+3 = 9 ohms
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6 ohms is in series with R1 so
Rtotal= 4+6=10 ohms
itotal= (\frac{Vtotal}{Rtotal})
= 120 v/10 ohms = 12 A
i total = i1 because all the current flows through it
i1= 12A
so the current splits into i2 and i3 and the amount of current that flows through a branch depends on the total resistance in each branch.
we already calculated the resistance in the R3+R4 & R2 branch as 6 ohms
since r3 and r4 are in series, the same current will flow through them
r3+r4 = 9 ohms
r2= 18 ohms
so the current in r2 will be half that of R3 & R4 (V=IR)
using the current divider rule
i2= 12A x (6 ohms/18 ohms)= 4 A
i3= 12A x (6 ohms/9 ohms) = 8 ohms