Question

(50pts) WAYYYYY overdue science assignment, NEED help with force vectors ASAP!

Example A In Example A the first vector is 27° with a force of 23 N. The second vector us 75° with a force of 30 N. Use 10 N = 1 cm as your scale. What is the resulting vector?

Example B
In Example B the first vector is 224° with a force of 27 N. The second vector is 123°, with a force of 32 N. What is the resulting vector?

Example C
In example C the first vector is 80° with a force of 16 N. The second vector is 144° with a force of 48 N. What is the force and degrees of the resulting vector?

Answer 1

Example A : 2.83 i + 3.94 j

Example B : -35.7 i + 6.5 j

Example C : 56.85 N, 50.71 °

Explanation:

since all vectors are given in terms of magnitude and angle polar coordinates are the obvious choice.

A vector r with magnitude r and angle θ can be represented in polar coordinates as

r = rcosθ i + rsinθ j

where i and j are unit vectors in x , y direction

let's look at the question now ,

Example A

two vectors are given lets call the a and b

a = 23 cos27° i + 23 sin27° j = 20.5 i + 10.4j

b = 30 cos75° i + 30sin75° j = 7.8 i + 29.0 j

resultant vector,a + b =( 20.5 + 7.8 )i + (10.4 + 29.0)j

= 28.3 i + 39.4 j

if we give the scale 10 N = 1 cm vector will become

r = 2.83 i + 3.94 j

Example B

two vectors are given lets call the a and b

a = 27 cos224° i + 27 sin224° j = -19.4 i + -18.7j

b = 30 cos123° i + 30sin123° j = -16.3 i + 25.2 j

resultant vector,a + b =( -19.4 + -16.3 )i + (-18.7 + 25.2)j

=-35.7 i + 6.5 j

Example C

two vectors are given lets call the a and b

a = 16 cos80° i + 16sin80° j = 2.8 i + 15.8j

b = 48 cos144° i + 48sin144° j = -38.8 i + 28.2 j

resultant vector, a + b =( 2.8 + -38.8)i + (15.8 + 28.2)j

= 36.0 i + 44.0 j

magnitude, | a + b | =
`\sqrt{x^(2)+y^(2)  }`

=
`\sqrt{36^(2)+44^(2)  }`

= 56.85 N

angle =
`tan^(-1) ((y)/(x) )`

=
`tan^{-1(44)/(36) }`

= 50.71 °