Final answer:
The Ground Reaction Force must generate a moment to counteract the body tipping forward when the Center of Mass is in front of the foot. In the example of a horse with its COM midway between its feet, each foot bears half the weight of the horse and rider. The coefficient of friction is calculated to prevent slipping based on horizontal forces and GRF.
Step-by-step explanation:
When considering the Ground Reaction Force (GRF) in the gait cycle, if the Center of Mass (COM) is in front of the foot, the GRF typically must generate a moment that will counteract the tendency of the body to tip forward. This moment is created because the line of action of the GRF lies behind the Centre of Mass, providing a stabilizing torque. In the case of a horse with its COM between its two supporting feet, as described in the question, there is a similar principle in play. Each foot would experience its share of support for the combined mass of the horse and rider.
The magnitude of GRF can be calculated using Newton's second law (Fnet = ma), where the force is equal to the mass times the acceleration due to gravity, g. In this static scenario, the vertical component of the GRF would exactly counterbalance the weight of the horse and rider system. So, for a horse and rider with a mass of 500kg, the GRF on each foot would be half the total weight, assuming the weight is evenly distributed.
Moreover, the adequate coefficient of friction required to prevent slipping would depend on the horizontal components of the forces involved, including any horizontal forces exerted, such as those from pushing against a wall. This coefficient can be determined to ensure that the horizontal GRF component does not exceed the frictional force limit.