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Gravitational force is a fundamental concept in physics that refers to the attractive force between two masses. For an object near the Earth's surface, this force depends on the object's mass and the acceleration due to gravity. This force can be calculated using the formula:
\[ F_g = m \times g \]
Where:

• \( F_g \) is the gravitational force
• \( m \) is the mass of the object
• \( g \) is the acceleration due to gravity, approximately \( 9.8 \text{ m/s}^2 \) on Earth

In our exercise, the mass of the boy is given as \( 30 \text{ kg} \). Using the formula, we can calculate the gravitational force acting on him: \( F_g = 30 \times 9.8 = 294 \text{ N} \). This force acts downward, keeping the boy attracted to Earth. Understanding gravitational force helps in analyzing the object's motion, especially when other forces come into play.

Newton's second law of motion is a key principle that explains how the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The law is represented by the equation:
\[ F_{net} = m \times a \]
Where:

• \( F_{net} \) is the net force applied to the object
• \( m \) is the mass of the object
• \( a \) is the acceleration of the object

In the context of our problem, an elevator accelerates upward at \( 0.5 \text{ m/s}^2 \). For the \( 30 \text{ kg} \) boy standing on the scale, the net force due to this acceleration can be computed as \( F_{net} = 30 \times 0.5 = 15 \text{ N} \). This net force affects how much extra force the scale reads from the boy, as it must account for both the gravitational force and the additional force from acceleration.

Elevator physics focuses on how different forces act on objects within an accelerating elevator. When an elevator accelerates upwards, as in our example, the experience alters how an object's weight is perceived.
An accelerating elevator exerts additional upward force on objects inside. This makes them feel 'heavier' due to the combined effect of gravity and the elevator's acceleration. To find the force read by the scale inside, we add the gravitational force and the force due to the elevator's acceleration:

• Gravitational Force: \( 294 \text{ N} \)
• Additional Force: \( 15 \text{ N} \)
• Total Force (Scale Reading): \( 294 + 15 = 309 \text{ N} \)

Understanding these forces helps predict what happens to an object's weight during vertical acceleration, which is a common situation in elevator physics.

The concept of normal force is crucial in understanding interactions between surfaces, especially in cases like our elevator scenario. Normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it.
In the case of an elevator accelerating upward, the normal force becomes greater than the gravitational force acting on the object. This is because the normal force must not only counteract gravity, but also provide the additional upward force required to accelerate the object:
For the boy in the elevator, the normal force \( F_n \) is calculated by adding the gravitational force \( F_g \) and the acceleration force \( F_{net} \):

• \( F_n = F_g + F_{net} = 294 + 15 = 309 \text{ N} \)

This increased normal force is what the scale measures, indicating the boy's apparent weight in the accelerating elevator. The concept is essential for solving many problems involving steady or changing motion, helping us understand the principles of force and equilibrium.