Three strings are attached to an object. If one of the strings is pulled north with a force of 10 N and one of the other strings is pulled west with 15 N, what force must be applied to the third string so that the object does not move?
Please help me with this question! I am ok with vector questions but I don't know what to do with this one. I tried a couple of times and I couldn't get the right answer.
Pull south with 10 N
Pull east with 15 Newtons
If you are doing this on an x y axis system then
Fx = 15
Fy = -10
|F| = sqrt(225 + 100) = sqrt (325) = 18.03
tan theta = Fy/Fx = -10/15
F1+F2 = -15+10i =18N.[-33.7o]=18N.[33.7o] N. of W. = 18N.[146.3o]CCW.
F3 must be equal in magnitude to F1+F2 but opposite in direction:
F3 = 18N.[33.7o] S. of E. = 18N.[146.3+180] = 18N.[326.3o] CCW.
The system is in Equilibrium; therefore, the object does not move,
To solve this question, we need to use vector addition. Let's break down the given forces into their x and y components.
The force pulling north is 10 N. Since the north direction is vertically upward, the force can be represented as (0, 10 N), where the x-component is 0 and the y-component is 10 N.
The force pulling west is 15 N. Since the west direction is horizontally to the left, the force can be represented as (-15 N, 0), where the x-component is -15 N and the y-component is 0.
Let F represent the force applied to the third string. We want the object to stay at rest, which means the net force on the object should be zero.
To find the net force, we add the x-components and the y-components separately. The x-components should sum to zero, and the y-components should sum to zero.
Sum of x-components: 0 + (-15 N) + x-component of F = 0.
Since the x-components of the given forces sum to -15 N, the x-component of F should be 15 N to make the sum zero.
Sum of y-components: 10 N + 0 + y-component of F = 0.
Since the y-components of the given forces sum to 10 N, the y-component of F should be -10 N to make the sum zero.
Therefore, the force applied to the third string should be (15 N, -10 N), or 15 N west and 10 N south (opposite of north).