Answer:
a) 4.57 m/s^2
b) 556.1 N
c) No
d) Yes
Explanation:
from the question we are given the following
mass of each seat (M) = 11 kg
diameter of platform = 8 m
length of chain = 2.5 m
angle = 26 degrees
mass of each child (m) = 40 kg
acceleration due to gravity (g) = 9.8 m/s^2
we can get the tension in the vertical direction from the formula
T x cosθ = mg
T = mg / cos θ
also we can get the tension in the horizontal direction from the form[tex]\sqrt{x} \sqrt{(g x r x sin) / cos}[/tex]ula
T x sin θ = mv^2 / r ( from the formula for centrifugal force )
T = ( mv^2) / rsin θ
equating the 2 formulas for tension we have
mg / cos θ = (mv^2) / rsin θ
g / cos θ = (v^2) / rsin θ
sin θ / cos θ = v^2) / gr
v = [tex]\sqrt{(g x r x sin θ ) / cos θ }[/tex] ....equation B
now lets calculate for r so we can substitute all values into the equation above
from the diagram below, the total extension of the seats from the center of the platform is =d/2 + (L x sinθ)
= 8/2 + (2.5 x sin 26) =4.38 m
now substituting all values into equation B we have
v = [tex]\sqrt{(9.8 x 4.38 x sin 26 ) / cos 26 }[/tex]
v = 4.57 m/s^2
b) tension in the chain is gotten by using the formula for tension
T cos θ = (M +m) x g
T = ((M +m) x g) / cos θ
T = ((40 +11) x 9.8) / cos 26
T = 556.1 N
c) Since the formula used to calculate the speed ( v = [tex]\sqrt{(9.8 x 4.38 x sin 26 ) / cos 26 }[/tex] ), consists of the mass, the speed does not depend on the mass.
d) Since the formula used to calculate the tension ( T = ((M +m) x g) / cos θ ) consist of the mass, the tension does depend on the mass.
