four forces act on a hot air ballon
356 N north
129 N west
297 N east
156 N south
a)find the magnitude of the resultant force on the balloon.
i already found this one out.
i got magnitude to be 261.197N
b) find the direction of the resultant force (in relation to the 297 N force, with up being positive)
i cant figure this one out
may someone please help me
change the S to -N, and the E to -W
356N-156N + 129W - 297W
Now get the N, W components..
200N - 168W. SO it is towards the NE, the angle will be arctan 200/168
check my math, I did it in my head.
yeah the math is right.
but i don't get this part:
ok i know that to solve for angle "a'
tan(a) = 200/168
a = arctan(200/168)
a = arctan(1.19047619)
a = ?????
what is arctan?
is it the same as doing tangent(1.1904)
arctan is the angle whose tangent is ....
Some use invtan meaning the same.
Some write it like this tan^-1 (xxxx)
oh!!! ok thank you
yeah we use tan^-1
i was confused on what arctan meant
but thanks
Certainly! To find the direction of the resultant force on the balloon, you can use geometry and trigonometry.
Step 1: Identify the x and y components of each force.
Let's break down each force into its x-component (horizontal direction) and y-component (vertical direction).
- The 356 N force acting north does not have any x-component since it only acts in the y-direction.
- The 129 N force acting west only has an x-component since it acts solely in the horizontal direction.
- The 297 N force acting east only has an x-component since it also acts solely in the horizontal direction.
- The 156 N force acting south does not have any x-component.
Therefore:
- The x-component of the 129 N force is -129 N (west is considered negative).
- The x-component of the 297 N force is 297 N (east is considered positive).
Step 2: Calculate the resultant x and y components.
The resultant x-component can be found by adding the x-components of the forces, and the resultant y-component can be found by adding the y-components:
Resultant x-component = (-129 N) + (297 N) = 168 N
Resultant y-component = 356 N - 156 N = 200 N
Step 3: Find the magnitude and direction of the resultant force.
To find the magnitude of the resultant force, you can use the Pythagorean theorem:
Magnitude (R) = sqrt((Resultant x-component)^2 + (Resultant y-component)^2)
Magnitude (R) = sqrt((168 N)^2 + (200 N)^2)
Magnitude (R) = sqrt(28224 N^2 + 40000 N^2)
Magnitude (R) = sqrt(68224 N^2)
Magnitude (R) = 261.2 N (approximated to one decimal place, which matches your previous calculation)
To find the direction of the resultant force in relation to the 297 N force, you can use trigonometry. Since the 297 N force is acting horizontally (x-direction), we only need to consider the x-component of the resultant force:
Direction (θ) = arctan(Resultant y-component / Resultant x-component)
Direction (θ) = arctan(200 N / 168 N)
Direction (θ) = arctan(1.19)
In this case, calculating the arctan (inverse tangent) of 1.19 will give you the angle in radians. To convert it to degrees, you can multiply it by 180/π (approximately 57.3).
Direction (θ) ≈ 48.7° (rounded to one decimal place)
Therefore, the direction of the resultant force relative to the 297 N force (with up being positive) is approximately 48.7°.