A fire helicopter carries a 679 kg bucket of water at the end of a 15.2 m long cable. Flying back from a fire at a constant speed of 42.5 m/s, the cable makes an angle of 49.0o with respect to the vertical. Determine the force of air resistance on the bucket.
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To determine the force of air resistance on the bucket, we need to first calculate the tension in the cable.
We can start by drawing a free-body diagram for the bucket. There are two forces acting on the bucket: the force of gravity pulling it downward (its weight), and the tension force in the cable pulling it upward.
The weight of the bucket can be calculated using the formula:
Weight = mass * gravity
Given that the mass of the bucket is 679 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 679 kg * 9.8 m/s^2 = 6654.2 N
Since the cable makes an angle of 49.0 degrees with respect to the vertical, we can decompose the weight into two components: one parallel to the cable (Tension) and one perpendicular to the cable (Weight * sin(angle)).
Let's calculate the tension force in the cable:
Tension = Weight * cos(angle)
Tension = 6654.2 N * cos(49.0 degrees) = 4355.1 N
Now that we have the tension in the cable, we can determine the force of air resistance on the bucket. Since the helicopter is flying at a constant speed, the force of air resistance is equal in magnitude and opposite in direction to the tension force.
Therefore, the force of air resistance on the bucket is 4355.1 N.