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The weight of an object is the force with which it is pulled towards the Earth due to gravity. It is calculated using the formula:

• \( W = m \cdot g \)

where \( m \) is the mass of the object and \( g = 9.8 \text{ m/s}^2 \) is the acceleration due to gravity.
It is important to remember that weight is a force and is measured in Newtons (N).
Thus, to calculate the weight of an object like a rock, you need to know its mass. For example, if a rock has a weight of 138 N, you can find its mass by rearranging the formula to \( m = \frac{W}{g} \).
This calculation shows that the mass of the rock is approximately 14.08 kg.

Effective weight refers to the way your body feels, depending on whether you're accelerating or decelerating. It changes depending on movement and the forces acting on the object.
Effective weight can be more or less than the actual gravitational force due to additional accelerations.

• When you accelerate upwards, like a rock being thrown upwards, your effective weight feels heavier due to additional forces.
• Conversely, when there is downward acceleration, it feels lighter.

To calculate effective weight under different accelerations, use the equation:

• \( F_{\text{effective}} = m \cdot (g + a) \) for upward acceleration, and
• \( F_{\text{effective}} = m \cdot (g - a) \) for downward acceleration.

This ensures you account for the changes brought about by acceleration.

Acceleration influences how heavy or light you feel, creating an effect on your perceived weight. When you're accelerating:

• Upwards, the acceleration adds to the gravitational pull, making the object feel heavier.
• Downwards, it subtracts from gravitational pull, causing a lighter feeling.

For example, if a rock usually under the force of gravity accelerating up at 12 m/s², the effective force of weight becomes greater. Simply calculate using:

• \( F = m \cdot (g + a) \)

With a downward acceleration, this works differently, as you subtract the outside acceleration from gravitational force:

• \( F = m \cdot (g - a) \)

Therefore, understanding these principles clarifies how movement affects weight sensation.

Gravitational force is the natural force exerted by the Earth pulling objects towards its center. It keeps objects anchored and creates the sensation of weight. Gravity provides a constant acceleration of 9.8 \( \text{m/s}^2 \).
You experience this force uniformly, whether moving or at rest.
It is important to recognize that gravity remains constant while acceleration changes. The gravitational force acts as the baseline upon which to calculate effective weight when additional forces like acceleration are present.
When the question involves movement or different forces, we adjust our calculations for these conditions but always start with the gravitational factor. Understanding gravity's role makes it easier to predict changes in effective weight under different circumstances.