A fire helicopter carries a 580 kg bucket at the end of a cable 20.0 m long as i

Question

A fire helicopter carries a 580 kg bucket at the end of a cable 20.0 m long as in figure p6.36. As the helicopter files at a constant speed of 38.0 m/s, the cable makes an angle of theta = 42.0 degree with respect to the vertical. The bucket presents a cross sectional area of 4.00 m^2 in a plane perpendicular to the air moving past it. Determine the drag coefficient assuming that the resistive force is proportional to the square of the bucket?s speed. A door in a hospital has a pneumatic closer that pulls the door shut such that the doorknob moves with constant speed over most of its path. (a) In this part of its motion, does the doorknob experience a centripetal acceleration? (b) Does it experience a tangential acceleration?

Explanation / Answer

your forces are tension, which extends 38 degrees from vertical. gravity, which is equal to mg and extends straight down, and air resistance which extends 180 degrees from the positive x axis.

if you make a chart, it should look like,

force x y
air -air 0
gravity 0 -mg
tension Tsin38 tcos38

now you add up each colunm and set them equal to mas times acceleration in that direction

m(accel in x direction)= tsin38 - air

m(accel in y direction)= tcos38 - mg

since the object is not accelerating at all, both accelerations are zero and you have:

tsin38=air

tcos38=mg

using the second equation you can solve for t and then plug that into the first equation to solve for the force of air resistance, which comes out to be 4287.7 Newtons

m*ax=T sin 420-air resistance

m*ay=T cos 420-mg

as the object is not accelerating at all,

T cos 420=mg

T sin 420=air resistance

Put value of T from first equation in the second equation, we get;

mg sin 420/ cos 420= air resistance

580 kg*9.8 m/s2* 0.6691/0.7431= air resistance

Air resistance=5117.97 N

Now drag coefficient is given by;

Drag coefficient=2*Air resistance/ mass density*(velocity)2*Area

Drag coefficient=2*5117.97 N / 1.2754 kg/m3*(38.0 m/s)2*4 m2

Drag coefficient=1.3894 N.m/kg

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