A force of 193 pounds makes an angle of 79°14' with a second force. The resultant of the two forces makes an angle of 27°0' to the first force. Find the magnitudes of the second force and of the resultant.
Answer:
magnitudes of the second force (vector) is 110.84 lb
the resultant force force has a magnitude of 239.85 lb
Step-by-step explanation:
Given that;
Magnitude of resultant vector R = ?
Direction of resultant vector α = 27°0'
Magnitude of vector p = 193
Magnitude of vector Q = ?
Angle between two vectors ∅ = 79°14'
Using the formula
tan∝ = [ Qsin∅ / P + Qcos∅]
tan27°0' = [ Qsin79°14' / 193 + Qcos79°14' )
we cross multiply
(193tan27°0') + (Qcos79°14'tan27°0' ) = Qsin79°14'
Q = 193tan27°0' / (sin79°14' - cos79°14'tan27°0')
Q = 110.84 lb
Therefore magnitudes of the second force (vector) is 110.84 lb
Now
R = √( p² + Q² + 2PQcos∅ )
R = √( 193² + 110.84² + ( 2 × 193 × 110.84 × cos79°14'))
R = 239.85 lb
Therefore the resultant force force has a magnitude of 239.85 lb
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