A 6490 kg helicopter accelerates upward at 0.59 m/s2 while lifting a 1180 kg car.

(a) What is the lift force exerted by the air on the rotors?
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(b) What is the tension in the cable (ignore its mass) that connects the car to the helicopter?

To find the lift force exerted by the air on the rotors, we need to first calculate the net force acting on the helicopter.

(a) The net force can be calculated using the equation:

Net Force = (Mass of Helicopter) × (Acceleration)

Given:
Mass of Helicopter = 6490 kg
Acceleration = 0.59 m/s^2

Plugging in the values, we can calculate the net force:

Net Force = (6490 kg) × (0.59 m/s^2)
= 3825.1 N

Since the lift force exerted by the air on the rotors is acting in the opposite direction to the weight of the helicopter, it can be considered the same as the net force:

Lift Force = Net Force
= 3825.1 N

Therefore, the lift force exerted by the air on the rotors is approximately 3825.1 N.

(b) To find the tension in the cable connecting the car to the helicopter, we need to consider both the weight of the car (acting downward) and the net force acting on the car (acting upward). The tension in the cable can be calculated as the sum of these forces:

Tension = Weight of Car + Net Force on Car

First, we find the weight of the car using the equation:

Weight of Car = (Mass of Car) × (Acceleration due to Gravity)

Given:
Mass of Car = 1180 kg
Acceleration due to Gravity ≈ 9.8 m/s^2

Weight of Car = (1180 kg) × (9.8 m/s^2)
= 11524 N

Next, we find the net force on the car using the equation:

Net Force on Car = (Mass of Car) × (Acceleration)

Given:
Acceleration = 0.59 m/s^2

Net Force on Car = (1180 kg) × (0.59 m/s^2)
= 696.2 N

Finally, we can calculate the tension in the cable:

Tension = Weight of Car + Net Force on Car
= 11524 N + 696.2 N
≈ 12220.2 N

Therefore, the tension in the cable connecting the car to the helicopter is approximately 12220.2 N.