The net force acting on the object is 4000 N at an angle of 45 degrees with respect to the horizontal axis. The acceleration is 0.5 m/s², and the mass of the object is 8000 kg.
Draw a free body diagram of the object and label all the forces acting on it:
^ Frozm = 8000 N
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| Ftrict = 4000 N <---- O ----> F = ?
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v Fgrav = 8000 N
Determine the net force in the horizontal direction:
Net force in the x-axis: Fnetx = F - Ftrict
Determine the net force in the vertical direction:
Net force in the y-axis: Fnety = Frozm - Fgrav
Use the Pythagorean theorem to find the magnitude of the net force:
Fnet = sqrt(Fnetx^2 + Fnety^2)
Use the inverse tangent function to find the angle of the net force with respect to the horizontal axis:
θ = atan(Fnety / Fnetx)
Use Newton's second law of motion to relate the net force, the mass, and the acceleration of the object:
Fnet = ma
Substitute the values given in the problem and solve for the unknowns:
F = 4000 N
a = 0.5 m/s^2
m = 8000 kg
The direction of the net force is the same as the direction of the acceleration:
θ = 45 degrees