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zvonat [6]
4 years ago
6

An astronaut notices that a pendulum which took 2.45 s for a complete cycle of swing when the rocket was waiting on the launch p

ad takes 1.25 s for the same cycle of swing during liftoff.
What is the acceleration (m/s²) of the rocket?(Hint: Inside the rocket, it appears that g has increased.)
Physics
1 answer:
klio [65]4 years ago
5 0

Answer:

2.84 g's with the remaining 1 g coming from gravity (3.84 g's)

Explanation:

period of oscillation while waiting (T1) = 2.45 s

period of oscillation at liftoff (T2) = 1.25 s

period of a pendulum (T) =2π. \sqrt{\frac{L}{a} }

where

  • L = length
  • a = acceleration

therefore the ration of the periods while on ground and at take off will be

\frac{T1}{T2} =(2π \sqrt{\frac{L}{a1} } ) /  (2π\sqrt{\frac{L}{a2} })

where

  • a1 = acceleration on ground while waiting
  • a2 = acceleration during liftoff

\frac{T1}{T2} = \frac{\sqrt{\frac{L}{a1} }}{\sqrt{\frac{L}{a2} }}

squaring both sides we have

(\frac{T1}{T2})^{2} = \frac{\frac{L}{a1} }{\frac{L}{a2} }

(\frac{T1}{T2})^{2} = \frac{a2}{a1}

assuming that the acceleration on ground a1 = 9.8 m/s^{2}

(\frac{T1}{T2})^{2} = \frac{a2}{9.8}

a2 = 9.8 x (\frac{T1}{T2})^{2}

substituting the values of T1 and T2 into the above we have

a2 = 9.8 x (\frac{2.45}{1.25})^{2}

a2 = 9.8 x 3.84

take note that 1 g = 9.8 m/s^{2} therefore the above becomes

a2 = 3.84 g's

Hence assuming the rock is still close to the ground during lift off, the acceleration of the rocket would be 2.84 g's with the remaining 1 g coming from gravity.

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By definition, the electric force is given by:

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The factors that affect strength of the electric force between two objects are:

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A cup of hot coffee initially at 95 degrees C cools to 80 degrees C in 5 min while sitting in a room of temperature 21 degrees C
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Answer:

When the temperature of the coffee is 50 °C, the time will be 20.68 mins

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The temperature of the room = 21°C

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According to Newton's law of cooling;

\frac{dT}{dt} \alpha (T-21)\\\\\frac{dT}{dt} = k (T-21)\\\\\frac{dT}{T-21} = kdt\\\\\int\limits {\frac{dT}{T-21}}  =  \int\limits kdt\\\\Log(T-21) =kt +  Logc \\\\Log (\frac{T-21}{c} ) = kt\\\\T -21 = ce^{kt}\\\\At \ t = 0, T = 95\\\\95-21 = ce^0\\\\74 = c\\\\New, equation: T -21 = 74e^{kt}\\\\Again; when \ t= 5\ min, T = 80\\\\80 -21 = 74e^{5k}\\\\59 = 74e^{5k}\\\\e^{5k} = \frac{59}{74}\\\\ 5k = ln(\frac{59}{74})\\\\5k = -0.2265\\\\k = -0.0453

When the temperature is 50 °C, the time t in min is calculated as;

T -21 = 74e^{-0.0453t}\\\\50 -21 = 74e^{-0.0453t}\\\\29 = 74e^{-0.0453t}\\\\\frac{29}{74} = e^{-0.0453t}\\\\0.39189 = e^{-0.0453t}\\\\ln(0.39189 ) = {-0.0453t}\\\\-0.93677 = {-0.0453t}\\\\t = \frac{-0.93677}{-0.0453}\\\\ t = 20.68 \ mins

Therefore, when the temperature of the coffee is 50 °C, the time will be 20.68 mins

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