When a parachute opens, the air exerts a large drag force on it. This upward force is initially greater than the weight of the sky diver and, thus, slows him down. Suppose the weight of the sky diver is 950 N and the drag force has a magnitude of 1100 N. The mass of the sky diver is 96.9 kg. What are the magnitude and direction of his acceleration?
On earth, two parts of a space probe weigh 18000 N and 3100 N. These parts are separated by a center-to-center distance of 15 m and may be treated as uniform spherical objects. Find the magnitude of the gravitational force that each part exerts on the other out in space, far from any other objects.
To find the magnitude and direction of the skydiver's acceleration, we can 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.
The net force acting on the skydiver can be calculated by subtracting the drag force from the weight of the skydiver:
Net force = Weight - Drag force
Given:
Weight = 950 N
Drag force = 1100 N
Substituting these values into the equation:
Net force = 950 N - 1100 N
Net force = -150 N
The negative sign indicates that the net force is in the opposite direction of the positive direction we've chosen (usually upward). In this case, the negative direction represents the downward force acting on the skydiver.
Using Newton's second law, we know that the net force is equal to the mass of the skydiver multiplied by the acceleration:
Net force = mass × acceleration
Rearranging the equation to solve for acceleration:
Acceleration = Net force / mass
Plugging in the values:
Acceleration = -150 N / 96.9 kg
Calculating the acceleration:
Acceleration ≈ -1.55 m/s²
So, the magnitude of the skydiver's acceleration is approximately 1.55 m/s², and its direction is downward or in the negative direction.