91Ó°ÊÓ

Gravitational force is the natural force that attracts any two masses towards each other. It is responsible for giving us weight. The formula to calculate gravitational force on Earth is given by:
\[ \text{Weight} = m \times g \]
where:

• \( m \) is the mass of the object (in kilograms).
• \( g \) is the acceleration due to gravity, about \( 9.8 \text{ m/s}^2 \) on the surface of the Earth.

In our problem, the monkey's mass is \( 8 \text{ kg} \), so the gravitational force (or weight) acting on it is calculated as:
\[ \text{Weight} = 8 \text{ kg} \times 9.8 \text{ m/s}^2 = 78.4 \text{ N} \]
This force pulls the monkey downward.

The normal force is the force exerted by a surface to support the weight of an object resting on it. This force acts perpendicular to the surface. In the context of our elevator problem, the scale exerts the normal force on the monkey.
Typically, when an object is at rest or moving uniformly (not accelerating), the normal force equalizes the gravitational force. But when other accelerations are involved, as in our problem, the effective forces must be considered.
The normal force in an elevator can change based on the elevator’s motion:

• When an elevator accelerates upwards, the normal force increases, making the object feel heavier.
• When it accelerates downwards, the normal force decreases, making the object feel lighter.
• When it moves at constant velocity or remains stationary, the normal force equals the gravitational force.

Effective acceleration is essentially the resultant acceleration experienced by an object when additional accelerations are factored in alongside gravity. In our exercise, two accelerations impact the monkey:

• Gravitational acceleration \( g = 9.8 \text{ m/s}^2 \).
• Elevator’s upward acceleration \( \frac{1}{4} g = 2.45 \text{ m/s}^2 \).

The effective acceleration \( a_{eff} \) is the sum of these accelerations, since the elevator is moving upwards:
\[ a_{eff} = g + \text{elevator’s acceleration} \]
\[ a_{eff} = 9.8 \text{ m/s}^2 + 2.45 \text{ m/s}^2 = 12.25 \text{ m/s}^2 \]
The normal force (which will be the reading on the scale) can be found using this effective acceleration:
\[ \text{Normal Force} = m \times a_{eff} \] \[ \text{Normal Force} = 8 \text{ kg} \times 12.25 \text{ m/s}^2 = 98 \text{ N} \]
Thus, the scale reads \( 98 \text{ N} \) when the elevator accelerates upward.