A fire helicopter carries a 615 kg bucket of water at the end of a cable 19.5 m long. As the aircraft flies back from a fire at a constant speed of 40.5 m/s, the cable makes an angle of 35.2o with respect to the vertical. Calculate the force of air resistance on the bucket

The bucket experiences three forces:

(1) its weight, W = 615*9.8 = 6027 N down
(2) air resistance Fx, horizontal
(3) cable tension T

Write two force balance equations:
W = T cos 35.2
Fx = T sin 35.2

from which T can be eliminated, to give
Fx/W = tan 35.2 = 0.705

Solve for Fx

The length of the cable does not matter.

thanks a lot. that really helped.

Thankyou! I had same problem type but different numbers & all but this really helped! thankss.

4251.580811

To calculate the force of air resistance on the bucket, we need to break down the forces acting on the bucket and find the net force.

1. Weight: The weight of the bucket can be calculated using the formula: Weight = mass * acceleration due to gravity. Therefore, the weight of the bucket is:

Weight = 615 kg * 9.8 m/s^2 = 6039 N (Newtons)

2. Tension: The tension in the cable can be calculated using the formula: Tension = weight + force of air resistance. Since we are trying to find the force of air resistance, we can rewrite the equation as:

Force of air resistance = Tension - weight

3. Finding the tension: To find the tension in the cable, we can use trigonometry. The tension can be determined by resolving the vertical and horizontal components of the tension.

Vertical component of tension = Tension * cos(angle)
Horizontal component of tension = Tension * sin(angle)

4. Using the Pythagorean theorem, we know that:
(Tension)^2 = (Vertical component of tension)^2 + (Horizontal component of tension)^2

Substituting the formulas from step 3 into the Pythagorean theorem equation, we get:
(Tension)^2 = (Tension * cos(angle))^2 + (Tension * sin(angle))^2

5. Simplifying the equation:
(Tension)^2 = Tension^2 * cos^2(angle) + Tension^2 * sin^2(angle)

Simplifying further:
Tension^2 = Tension^2 * (cos^2(angle) + sin^2(angle))

From the equation, we can see that Tension^2 cancels out, leaving us with:
1 = cos^2(angle) + sin^2(angle)

Since cos^2(angle) + sin^2(angle) = 1, we can conclude that Tension = Tension. This means that the tension in the cable is equal to the weight of the bucket.

6. Substituting the values into the equation:
Force of air resistance = Tension - weight
Force of air resistance = 6039 N - 6039 N
Force of air resistance = 0 N

Therefore, the force of air resistance on the bucket is 0 N.