Final answer:
The upward force exerted by the air on the open parachute is calculated using Newton's second law and subtracting the net force (due to downward acceleration) from the gravitational force. The upward force is found to be 589.56 N.
Step-by-step explanation:
Calculating the Upward Force on a Parachute
To calculate the upward force exerted by the air on the parachute, we need to consider the forces acting on the system (person + parachute) and the net acceleration. The system is composed of the person with a mass of 81 kg and the parachute with a mass of 5.7 kg. The total mass is therefore 81 kg + 5.7 kg = 86.7 kg. Given that the system is accelerating downwards at 3.0 m/s2, we can use Newton's second law of motion to find the net force.
Newtons's second law states that the net force is equal to the mass multiplied by the acceleration (F = ma). The gravitational force (weight) can be calculated using the formula Fg = m * g, where m is the total mass and g is the acceleration due to gravity (9.8 m/s2). Thus, Fg = 86.7 kg * 9.8 m/s2 = 849.66 N. The net force (Fnet) acting on the system is the mass times the given downward acceleration, so Fnet = 86.7 kg * 3.0 m/s2 = 260.1 N downward.
To find the upward force from the air (Fair), we recognize that it is the difference between the gravitational force and the net force: Fair = Fg - Fnet. Substituting in the known values, we get Fair = 849.66 N - 260.1 N = 589.56 N. Therefore, the upward force on the open parachute from the air is 589.56 N.