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Given: g = 9.8 m/s 2 . A small glass of water is placed on carousel inside a microwave oven, at a radius 6.5 cm from the center. The carousel rotates steadily, tuning through one revolution every 9.3 s. What angle does the water surface make with the horizontal? Answer in units of ◦ .

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usmanbiu

Answer:

0.17 degrees

Explanation:

From the question we are given the following:

acceleration due to gravity = [tex]9.8 \frac{m}{s^{2} }[/tex]

radius (r) = 6.5 cm = 0.065 m

time (s) = 9.3 s

angle = ?

  • we first have to calculate the distance the water moves, and this is the circumference of the microwave

         circumference = 2 x π x r = 2 x π x 0.065 = 0.408 m

  • Now we find the speed with which it moves at

            speed = [tex]\frac{distance}{time}[/tex]

                         =  [tex]\frac{o.408}{9.3}[/tex] = 0.044

  • The next step is to find the centripetal acceleration

         a = [tex]\frac{v^{2} }{r}[/tex]

              = [tex]\frac{0.044^{2} }{0.065}[/tex] = 0.03

being a vector quantity, acceleration has direction, the centripetal acceleration is the x component while the y component would be the acceleration due to gravity (g)

A = 0.03 x + 9.8 y

to find the angle we can apply tan θ = [tex]\frac{ 0.03 }{9.8[/tex]

     θ  = 0.17 degrees

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