When a parachute opens, the air exerts a large drag force on it.This upward force is initially greater than the weight of the skydiver and, thus, slows him down. Suppose the weight of the skydiver is 956 N and the dragforce has a magnitude of 1005 N. The mass of the sky diver is 97.6 kg. What are the magnitude and direction of his acceleration?
The net force is 49 N (up). Divide that by the mass to get the acceleration, which will be in the same direction.
Note that the deceleration will reduce the drag until it equals the weight. The deceleration you compute here will not be constant.
To find the magnitude of the skydiver's acceleration, we can use Newton's second law of motion, which states that force is equal to mass times acceleration (F = m * a).
Given:
Weight (W) = 956 N
Drag force (F) = 1005 N
Mass (m) = 97.6 kg
The weight of the skydiver can be considered as a downward force acting on the skydiver. The drag force can be considered as an upward force acting on the skydiver. Since the drag force is initially greater than the weight, it will slow down the skydiver's acceleration.
To determine the magnitude of the acceleration (a), we subtract the weight from the drag force:
a = (F - W) / m
= (1005 N - 956 N) / 97.6 kg
Calculating the magnitude of the acceleration:
a = 49 N / 97.6 kg
≈ 0.50 m/s²
The direction of the acceleration will be upward, opposite to the direction of the weight, since the drag force is acting in the opposite direction to the downward weight force.
To find the magnitude and direction of the skydiver's acceleration, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's identify the known values:
- Weight of the skydiver = 956 N
- Drag force = 1005 N
- Mass of the skydiver = 97.6 kg
Since the drag force is directed upward and is initially greater than the weight of the skydiver, the net force acting on the skydiver is the difference between these two forces:
Net force = Drag force - Weight
Substituting the given values:
Net force = 1005 N - 956 N = 49 N (upward)
Now, we can calculate the acceleration using Newton's second law. Rearranging the equation, we have:
Acceleration = Net force / Mass
Substituting the calculated values:
Acceleration = 49 N / 97.6 kg ≈ 0.502 m/s² (upward)
Therefore, the magnitude of the skydiver's acceleration is approximately 0.502 m/s², and the direction of the acceleration is upward.