need 4 answers Question 3, chap 103, sect 7. part 1 of 210 points Consider four

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need 4 answers

Question 3, chap 103, sect 7. part 1 of 210 points Consider four vectors F, F2, F3, and 4, where their magnitudes are Fi - 59 N, 160°, :3-22°, and 4--60°, measured from the positive x axis with the counter-clockwise angular direction as positive What is the magnitude of the resultant vec- tor F, where F- Fi F2 + F3 + F4 Answer in units ofN Question 4, chap 103, sect 7. part 2 of 210 points What 1s the direction of this resultant vec - tor F? Note: Give the angle in degrees, use coun- terclockwise as between the limits of -180° and +180° fronm the positive x axis Answer in units of° the positive angular directio n,

Explanation / Answer

Q3.

1.

given

F1 = 59 N, theta1 = 130 deg

F2 = 31 N, theta2 = -160 deg

F3 = 17 N, theta3 = 22 deg

F4 = 48 N, theta4 = -60 deg

now, to add these forces in vector notation

we assume ia nd ja re unit vectors along x and y directions

hence

F = F1 + F2 + F3 + f4

F = F1(cos(theta1)i + sin(theta1)j) + F2(cos(theta2)i + sin(theta2)j)+ F3(cos(theta3)i + sin(theta3)j) + F4(cos(theta4)i + sin(theta4)j)

hence

F = -27.292814i -0.6069095 j

hence magnitude = |F| = 27.299561 N

2. the direction of the force can be given by

theta = arctan(Fy/Fx) = 181.27387 deg with the +ve x axis in anticlockwise direction

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