Final answer:
With a pushing force of 150N to the left and 120N to the right, the net force on the cart is 30N to the left, resulting in the cart moving to the left. However, any additional forces, like friction, must also be considered to fully determine the cart's motion.
Step-by-step explanation:
If Willie pushes a cart with 150N of force to the left and Biff pushes the same cart with 120N of force to the right, we apply Newton's First Law of Motion to describe the motion of the cart. Since both forces are applied horizontally and in opposite directions, we calculate the net force on the cart by subtracting the smaller force from the larger one. The net force acting on the cart would be 30N to the left (150N - 120N = 30N), as Willie's force is greater. This net force would result in an acceleration of the cart to the left, unless there are other forces present, like friction, which may alter the actual motion of the cart.
When considering the example of a physics professor who exerts a backward force of 150N on the floor and all opposing forces such as friction total 24.0N, the net horizontal force on the system consisting of the professor, cart, and equipment would be the difference between the force exerted by the professor's feet on the floor and the opposing frictional force. This means that if the professor alone were pushing the cart and equipment, the net force would be 126N forward (150N - 24N).