To find the friction force without knowing the coefficient of friction or acceleration, one can utilize a bathroom scale to measure the weight of an object, which equals the force of gravity. By attaching the scale to the object and gradually increasing the slope of the surface until the object begins to slide, the static frictional force can be determined using the angle of inclination. Alternatively, a ticker timer experiment can be conducted where the object is pulled by a known weight, allowing for the calculation of kinetic friction if acceleration is measured. The discussion emphasizes the importance of encouraging critical thinking in problem-solving rather than providing direct answers. Understanding the relationship between weight, gravitational force, and the necessary conditions for movement is crucial in determining frictional forces.