Final answer:
The motion of a box pushed off a table is primarily due to gravity, with Newton's First Law of Motion (law of inertia), friction, and the box's inertia also playing roles. Friction is an external force acting in the direction opposite to the object's motion, and the behavior of two balls thrown in the air can vary due to different external factors despite gravity being constant.
Step-by-step explanation:
When a box is pushed off a table and two different and opposing forces are exerted on it, the box will begin to move due to the imbalance of forces. According to Newton's First Law of Motion, or the law of inertia, an object will remain at rest or move at a constant velocity unless acted on by an outside force. In this scenario, gravity acts as the external force that causes it to fall, illustrating that the object moves primarily due to gravity. It could be argued that all listed factors – Newton's First Law, gravity, friction, and inertia – contribute to the motion of the box, but gravity is the primary cause of the downward movement once the box is pushed off the table.
As for the question on friction, it is an external force that opposes motion by acting in the direction opposite to the motion of the object. When two people apply the same force to throw two identical balls in the air, the balls will not necessarily travel the same distance because there might be external factors such as air resistance affecting each ball differently, despite the gravitational force being the same.
In the case of the ball rolling from north to south, the frictional force acts in the opposite direction, from south to north. If two people push a cart on a horizontal surface applying forces F₁ and F₂ in the same direction, the magnitude of the net force acting on the cart, Fₙᶜ, would be equal to F₁ + F₂ minus any frictional force acting against the motion.
When drawing a free-body diagram for a body with mass m being pushed along a horizontal surface by a force F and opposed by a frictional force f, you would show vectors representing each of these forces with their respective magnitudes and directions.
Lastly, Newton's third law of motion states that whenever a first body exerts a force on a second body, the first body experiences a force that is equal in magnitude but acts in the direction opposite the direction of the applied force.