A 100 N force acts along the x axis and a 150 N force acts at an angle of 40 degrees above the x axis.?
A 100 N force acts along the x-axis, while a 150 N force acts at an angle of 40 degrees above the x-axis.
a) What is the resultant force vector?
b) What is the magnitude of the resultant force?
c) What is the direction of the resultant force? (Hint: consider using the arctan function.)
3 Answers
The first step is to determine the x and y components of the 150 N force.
x = 150 * cos 40 â 115 N
y = 150 * sin 40 â 96.4 N
Total x = 100 + 150 * cos 40 â 215 N
F = â(Fx^2 + Fy^2)
F = â[(100 + 150 * cos 40)^2 + (150 * sin 40)^2]
This is approximately 236 N.
Tan θ = y ÷ x
Tan θ = (150 * sin 40) ÷ (100 + 150 * cos 40)
The angle is approximately 24.2Ë above horizontal .
The resultant force vector is approximately 236 N at angle of 24.2Ë above horizontal. I hope this is helpful for you.
You didnât tell whether the 150N is sorta helping the 100N or sorta opposing.
RealPro assumed the 150N acts so that its x axis component points the same direction as the 100N. If that is true, go with that advice. If it was the other way around, you should have told us which.
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