a force of 100N is the resultant of two force p and q. if p=50 and it makes angle of 20° with the resultant . find the magnitude of q
To find the magnitude of force q, we can use the concept of vector addition.
Let's assume force p and force q are two vectors which add up to give the resultant force of 100N.
First, let's break down force p into its horizontal and vertical components. The horizontal component of force p can be found by multiplying the magnitude of force p (50N) by the cosine of the angle it makes with the resultant (20°):
Horizontal component of p = 50N * cos(20°)
Similarly, the vertical component of force p can be found by multiplying the magnitude of force p (50N) by the sine of the angle it makes with the resultant (20°):
Vertical component of p = 50N * sin(20°)
Now, let's represent force p in terms of its components:
Force p = (Horizontal component of p) î + (Vertical component of p) ĵ
Where î represents the unit vector in the horizontal direction and ĵ represents the unit vector in the vertical direction.
Since force p and force q add up to give the resultant force, we can write the following equation:
Force p + Force q = Resultant force
(50N * cos(20°)) î + (50N * sin(20°)) ĵ + Force q = 100N
Now, let's equate the components of the vectors separately:
Horizontal component of p + Horizontal component of q = Horizontal component of the resultant
(50N * cos(20°)) + (Magnitude of q * cos(Θq)) = 100N * cos(θR)
Vertical component of p + Vertical component of q = Vertical component of the resultant
(50N * sin(20°)) + (Magnitude of q * sin(Θq)) = 100N * sin(θR)
In these equations, Θq represents the angle that force q makes with the resultant, and θR represents the angle of the resultant force.
Now, we can solve these two equations simultaneously to find the magnitude of force q and the angle it makes:
From the first equation:
(50N * cos(20°)) + (Magnitude of q * cos(Θq)) = 100N * cos(θR)
From the second equation:
(50N * sin(20°)) + (Magnitude of q * sin(Θq)) = 100N * sin(θR)
Once you plug in the values for cos(20°), sin(20°), 100N, and θR, you can solve these equations to find the magnitude of force q and the angle it makes.