(8%) Problem 8: You are constructing a mobile out of 5 identical toy helicopters
ID: 2041398 • Letter: #
Question
(8%) Problem 8: You are constructing a mobile out of 5 identical toy helicopters. each of mass m 28.9 g, 4 identical sticks (each length 22.1 cm, and negligible mass), and thin string of negligible mass. The distance from the left-hand side of cach stick to the attachment point of the sting supporting it arc x, through x4 respectively, as shown in the diagram. The tensions in the supporting strings are through T4 as shown. You want to design the mobile so that it is in static equilibrium T4 T3 T2 Otheexpertta.com 13% Part (a) Find the tension in Newtons in the string Grade Summary Deductions Potential Late Work % 50% Late Potential 50% 0% 400% sinO cosO tanO j ( acosO cotanO asin0 Submissions Attempts remaining: 3 (4% per attempt) detailed view atan)acotan)sinh) 23 cosh tanhO cotanh() °Degrees Radians Submit Hint I give up! Hints: 4% deduction per hint. Hints remaining: 5 Feedback: 5% deduction per feedback. 13% Part (b) Find the tension in Newtons in the string T2 13% Part (c) Find the tension in Newtons in the string T3 13% Part (d) Find the tension in Newtons in the string 14 13% Part (e) Find the distance x, in centimeters . I3% Part (f) Find the distance X2, in centimeters 13% Part (g) Find the distance x3, in centimeters ? 13% Part (h) Find the distance x4, in centimetersExplanation / Answer
In all cases the moments are taken about point of suspension
T4 = 28.9 X 10^(-3) Kg / Helicopter X 5 Heli X 9.8 m/s^2 = 0.28322 X 5 = 1.4161 N = 1.42 N
T3 = = 0.28322 X 4 =1.13 N
Taking moments,we get
T3 x X4 = 0.28322 X 4 28.9 X 10^(-3) Kg X 9.8 m/s^2 X [22.1X 10^(-2) - X4]
[1.13 N + 28.9 X 10^ (-3) X 9.8 ] x X4 = 28.9 X 10^(-3) X 9.8 X 22.1 X 10^(-2)
X4 = 0.06259162 / ( 1.13 +0.28) = 4.4 cm
T2 = 0.28322 X 3 = 0.849 N
T1 = 0.283 x 2 = 0.586 N
X3 ( 28.9 X 10^(-3) X 9.8) = 0.849 X [ 22.1 X 10^(-2) - X3]
solving X3 = 0.166 mrs = 16.6 cms
x2 [ 28.9 X 10^(-3) X 9.8 + 0.586 ] = 0.586 X[ 22.1 X 10^(-2) - X2]
solving for X2 = 0.149 mrs = 14.9 Cm
X1 = 22.1/2 = 11.05 cm, since both weights are equal
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