Question

Two forces, 80 N and 100 N acting at an angle of 60° with each other, pull on an object.
(a) What single force would replace the two forces?
(b.) What single force would balance the 2 forces?

Answer 1

its just adding vectors; assume one is pulling to the right along the positive x axis, and the other is pulling 60 degrees to it

Answer 2

80 cos(60) i + 80 sin(60) j
100 cos(0) i + 100 sin(0) j

the Force resulting is the magnitude (length) of the vector created by the addition

Answer 3

is this the answer for (a)?

Answer 4

its the answer for both of them ...

Answer 5

once you know the vector that is the result of these 2, then the canceling vector is just the same vector going in the opposite direction

Answer 6

what's the cancelling vector?

Answer 7

since the vector (a) is a single vector that can replace the actions of the first 2 vectors; then an equal but opposite vector will cancel it out.

Answer 8

if youve ever seen a game of tug of war ....

Answer 9

156.2 N is that for (a)

Answer 10

80 1/2 i + 80 sqrt(3)/2 j
100 i + 0 j
-----------------------
140 i + 40 sqrt(3) j

so the vector (140, 40sqrt(3)) is (a). we can scale this as: 20(7 , 2 sqrt(3))

the length of the vector is therefore: 20 sqrt(61) = 156.2 yes

Answer 11

what about (b)? i don't very much understand how to solve b.

Answer 12

the word balance, think of a set of scales ... they are balanced when the force on one side equals the force on the opposite side. In order to balance out the 2 given vectors, which can be replaced by the single vector: 20(7,2sqrt(3)) we would need to apply a vector of -20(7,2sqrt(3))

Answer 13

how do i solve for it using the trigonometric method?