91Ó°ÊÓ

When a skydiver opens their parachute, an interesting phenomenon occurs thanks to what's known as **drag force**. This force is essentially air resistance that acts in the opposite direction of the skydiver's motion. In the described scenario, the drag force reaches a magnitude of \(1027 \, \text{N}\), pointing upwards. This is a bit stronger than the simple weight force acting on the skydiver, which is \(915 \, \text{N}\) downward. So, what's going on here?
The drag force is pivotal because it impacts the speed and direction of the skydiver's movement. In this case, it is powerful enough to stop the skydiver from continuing downward at the same speed, resulting in a deceleration or a slowing down of the descent. This helps the skydiver come to a safer stop, using a natural counteracting force—air pressure. Without it, falling would be rapid and unsafe.

• Drag force acts against motion.
• Considerably contributes to slowing objects down.
• Its magnitude is influenced by speed and surface area.

The concept of **net force** is crucial here. Net force is basically the sum of all forces acting on an object—it determines the object's overall motion direction and acceleration. In this problem, we have two key forces: the drag force and the weight of the skydiver.

To determine the net force \( (F_{\text{net}}) \), we use the equation:
The net force is calculated by subtracting the weight from the drag force:
\[ F_{\text{net}} = F_{\text{drag}} - F_{\text{weight}} = 1027 \, \text{N} - 915 \, \text{N} = 112 \, \text{N} \]
This results in a **net force of 112 N upwards**, because the drag force exceeds the downward weight force. This means the overall force is upward, indicating upward acceleration.

• Net force determines motion.
• It helps define the overall direction of movement.
• A balance of forces implies zero net force and no acceleration.

Acceleration is a change in velocity and is directly linked to the forces at play through **Newton's Second Law**. This physical law states that the acceleration of an object is equal to the net force acting upon it, divided by its mass. It's a key player in determining how fast or slow the skydiver will change speed and direction.

The specific formula applied here is:
\[ a = \frac{F_{\text{net}}}{m} \]where \(a\) represents acceleration, \(F_{\text{net}}\) is the net force, and \(m\) is the mass of the skydiver. By inserting the solved value of net force (\(112 \, \text{N}\)) and the mass (\(93.4 \, \text{kg}\)) into the equation, we find:
\[ a = \frac{112 \, \text{N}}{93.4 \, \text{kg}} \approx 1.20 \, \text{m/s}^2 \]
This result reveals that the skydiver's acceleration is indeed upward at approximately \(1.20 \, \text{m/s}^2\).

• Newton's Second Law offers a blueprint for acceleration.
• Net force is critical in determining acceleration's direction and magnitude.
• Higher forces or lower mass result in greater acceleration.