A helicopter is used to fill buckets with water to drop on fires. The bucket is

Question

A helicopter is used to fill buckets with water to drop on fires. The bucket is a hemisphere with a diameter of 2 meters and a mass of 25 kg. The helicopter lowers the bucket into a lake or reservoir to fill it.

a) What is the weight of a bucketful of water?

b) Assume the full bucket starts at rest and the helicopter accelerates upward at 0.75 m/s2 . Calculate the tension in each of the five cables used to attach the bucket to the helicopter.

c) The helicopter has a mass of 1960 kg. Calculate the lift force produced by each of the four blades in order to allow the bucket-carrying helicopter to hover over the fire.

d) If the lift force from part c) is maintained once the water is dropped, how far does the helicopter displace in 0.5 seconds?

In this question do I need to find out spefic information about filling the bucket?

Explanation / Answer

Here ,
a)

volume of water , v = (2/3) * pi * r^3

V = (2/3) * pi * (2/2)^2

V = (2/3) * pi * 1^3

V = 2.094 m^3

mass of water , m = 25 + 2.094 * 1000

m = 2119 Kg

weight = 2119 * 9.8

weight = 20776 N

the weight of the bucket full of water is 20776 N

b)

let the acceleration is a

5*T = 2119 *(9.8 + 0.75)

T = 4471.1 N

the tension in each branch is 4471.1 N

c)

lift in each balde is F

4*F = 5 * T + m*g

4*F = 5 * 4471.1 + 1960 * 9.8

F = 10390.1 N

the lift force by each blade is 10390.1 N

d)

displacement = 0.5 * at^2

displacement = 0.5 * 0.75 * 0.5^2

displacement = 0.094 m

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