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Newton's First Law, often referred to as the law of inertia, explains the relationship between a moving object and the forces acting on it. It tells us that if there's no net external force acting on an object, the object will maintain its state of rest or continue moving at a constant velocity. In simpler terms, things keep doing what they are doing unless something makes them change.

In the context of the 5.0 kg bag of potatoes in our problem, this law implies that whether the shopping cart is stationary or moving at a constant velocity, the bag of potatoes will not experience any change in its motion horizontally. This is because the forces vertically balance each other out, and horizontally, there are no unbalanced forces acting on the bag. Since the cart is moving at a constant velocity, there is no horizontal acceleration, confirming that the net force is indeed zero.

Therefore, both when the cart is stationary and when it moves with a constant velocity, the free-body diagram remains unchanged, supported by Newton's First Law.

The normal force acts upon objects in contact with a surface, pushing up against them to support their weight. This force arises naturally as a reaction to the weight force, following Newton's Third Law, which states that every action has an equal and opposite reaction.

In the example of the bag of potatoes in the shopping cart, the normal force is exerted by the bottom of the cart. It acts upwards, effectively countering the downward gravitational pull on the potatoes. This ensures the bag doesn't simply fall through the cart! For a stationary object or one moving at constant velocity along a flat plane, like the shopping cart, the normal force and weight force balance each other out.

Knowing about normal force is crucial for sketching accurate free-body diagrams, as it helps us understand how objects rest on surfaces or interact with them without accelerating vertically.

Weight force, also known as gravitational force, is the force exerted by the Earth's gravity on an object with mass. It acts downward towards the center of the Earth and is calculated by multiplying the object's mass by the acceleration due to gravity, approximately 9.8 m/s² on Earth.

In our scenario, the weight force acts on the 5.0 kg bag of potatoes. By calculating it using the formula \( W = mg \), we find that the force is \( 5.0 \times 9.8 = 49 \, \text{N} \) directed downward. This weight is what presses the bag against the cart's bottom, necessitating the normal force to counterbalance it.

Understanding weight force is vital for constructing free-body diagrams. It helps visualize and quantify the gravitational effects on objects, ensuring they are in equilibrium, particularly when no motion change is detected, as per Newton's First Law.