To determine the magnitude of the largest force p that can be applied to the 56-kg cart without causing one of the wheel reactions to be zero, we need to consider the forces acting on the cart and the constraints on the motion of the cart.
First, we need to consider the forces acting on the cart. The weight of the cart, which is equal to the product of the mass of the cart and the acceleration due to gravity, acts downward on the cart. The applied force p acts on the cart in the direction specified. There may also be other forces acting on the cart, such as friction forces between the wheels and the ground, or forces due to the motion of the cart through a fluid.
Next, we need to consider the constraints on the motion of the cart. The wheels of the cart provide constraints on the motion of the cart because they only allow the cart to move in certain directions. The wheel reactions at a and b are the forces that the wheels exert on the cart to support its weight and the applied force p. The wheel reactions at a and b must be non-zero for the cart to be stable and not tip over.
To determine the magnitude of the largest force p that can be applied to the cart without causing one of the wheel reactions to be zero, we need to consider the balance of forces and the constraints on the motion of the cart. This requires solving a set of equations that describe the forces acting on the cart and the constraints on its motion. Without more information about the specific configuration of the cart and the forces acting on it, it is not possible to determine the magnitude of the largest force p that can be applied to the cart.