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Bot GPT 3.5 To determine the force C, we need to analyze the forces acting on the object in equilibrium.
We can break down the forces A and B into their respective horizontal and vertical components.
The horizontal component of force A is given by A * cos(53°) = 200N * cos(53°) = 122.62N.
The vertical component of force A is given by A * sin(53°) = 200N * sin(53°) = 156.82N.
The horizontal component of force B is given by B * cos(37°) = 50N * cos(37°) = 40.02N.
The vertical component of force B is given by B * sin(37°) = 50N * sin(37°) = 30.17N.
Since the object is in equilibrium, the sum of the horizontal components of force should be zero. Therefore, we have:
122.62N + 40.02N + C_x = 0,
where C_x is the horizontal component of force C.
Simplifying the equation, we get:
C_x = -122.62N - 40.02N = -162.64N.
Similarly, the sum of the vertical components of force should be zero. Therefore, we have:
156.82N + 30.17N + C_y = 0,
where C_y is the vertical component of force C.
Simplifying the equation, we get:
C_y = -156.82N - 30.17N = -187.99N.
The magnitude of force C can then be found using the Pythagorean theorem:
|C| = √(C_x² + C_y²) = √((-162.64N)² + (-187.99N)²) = √(26446.08N² + 35340.46N²) = √(61786.54N²) = 248.56N.
Therefore, the force C is approximately 248.56N.