91Ó°ÊÓ

Gravitational force is an essential concept in physics which explains the attraction between two masses. It acts in the direction of the mass experiencing the force. In this exercise, we're considering the force between Earth and both the person and their parachute.

The formula to calculate gravitational force is:

• \( F_{gravity} = m \cdot g \)

where:

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

This force makes objects fall when dropped. For the parachuting person, their mass is \( 80 \ \text{kg} \). Putting this into the formula gives \( F_{gravity, person} = 80 \ \text{kg} \times 9.8 \ \text{m/s}^2 = 784 \ \text{N} \).

Similarly, the parachute, with a mass of \( 5 \ \text{kg} \), experiences a gravitational force of \( 49 \ \text{N} \). This demonstrates the strong presence of gravity in terrestrial environments, pulling everything towards the center of Earth.

Net force is the overall force acting on an object when all individual forces are combined. It determines the object's motion, according to Newton's Second Law. This is represented by the equation \( F_{net} = (m_{total}) \cdot a \), where:

• \( m_{total} \) is the combined mass of the person and parachute, totaling \( 85 \ \text{kg} \)
• \( a \) is the acceleration, noted here as \( 2.5 \ \text{m/s}^2 \)

For our parachuting scenario, the net force includes both gravitational pull downward and any opposing forces, like air resistance. We can find the net force by summing up these elements:

• Total gravitational force downward: \( 833 \ \text{N} \)
• Calculation of \( F_{net} = 85 \ \text{kg} \times 2.5 \ \text{m/s}^2 = 212.5 \ \text{N} \) upward

Balancing these forces helps us calculate the upward force resisting gravity. Understanding net force is crucial to comprehending how objects move or remain in equilibrium.

Upward force refers to the force that counteracts the pull of gravity. In the context of the parachuting exercise, this force is provided by the air pushing against the open parachute. This upward force enables the parachute to slow down the descent of the person.

Using Newton's Second Law, the equation becomes:

• \( F_{air} = (m_{person} + m_{parachute}) \cdot a + F_{gravity, total} \)

By substituting the known values:

• \( F_{gravity, total} = 784 \ \text{N} + 49 \ \text{N} = 833 \ \text{N} \)
• \( (80 \ \text{kg} + 5 \ \text{kg}) \times 2.5 \ \text{m/s}^2 = 212.5 \ \text{N} \)
• Adding these forces gives \( F_{air} = 833 \ \text{N} + 212.5 \ \text{N} = 1045.5 \ \text{N} \)

This calculation shows the necessary upward force requisite to counteract gravitational forces, allowing the parachute to function effectively. Thus, the upward force is what primarily regulates the fall speed, ensuring safety and control for the parachutist.