Question

2) For the three force vectors in the x-y plane, a) Calculate the sum of the force vectors (R) by first calculating EF, and EFy (the scalar sums of the x and y force components, respectively) and then writing the vector result R in îjk summation format. Calculate the magnitude of the resultant,RI, and фх, the angle the resultant makes with the x- axis Sketch R and the angle φ b) c) 15 N 10 N 40 30° 35 12 N

need help with this problem

Answer 1

2

a) $10 N = 10 N cos 30 \boldsymbol{i} + 10 N Sin 30 \boldsymbol{j}$ ---- (1)

  $15N = -15 N cos 40 \boldsymbol{i} + 15 N Sin 40 \boldsymbol{j}$ ---- (2)

  $12N = -12 N sin 35 \boldsymbol{i} -12 N cos35 \boldsymbol{j}$ ------ (3)

Adding components along X and Y-axes

$R= 10Ncos30\boldsymbol{i}-15Ncos40^{i}-12 N sin 35 \boldsymbol{i} +10NSin30\boldsymbol{j}+15NSin40\boldsymbol{j}-12Ncos35\boldsymbol{j}$

R = -9.7 $\boldsymbol{i}$ + 4.8 $\boldsymbol{j}$

b)

I R I = sqrt [ (- 9.7)^2 + (+4.8)^2 ] = 10.8 N

$\theta =Arctan[4.8/(-9.7)]$ = 153.7 deg with respect to +ve X-axis ( or 26.3 degrees with respect to -ve X-axis )