howTo_solve - HOW TO SOLVE A PROBLEM An EXEMPLE to FOLLOW...

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HOW TO SOLVE A PROBLEM : An EXEMPLE to FOLLOW The problem : Using the universal law of gravity and the 2 nd law of motion of Newton Assuming the magnitude of your mass in kg is approximately equal to Your weight/2 in pounds. calculate a) the Acceleration of the earth gravity on your body b) the Acceleration on the earth due to your mass ======================================= The Answer: a) F = m you x a Earth Newton’s second law of motion with F the force between the interacting pair in (N) m you , your mass in (kg) a Earth , the acceleration due to Earth gravity in (m/s 2 ) ] 1 [ you Earth Earth you Earth you you Earth you m F a a m a m m F a m F = = / × / = × = On the other hand [2] 2 d m GM F you Earth = With F the force between the interacting pair in (N) M Earth the mass of the Earthg in (kg) m you , your mass in (kg) d the distance between the interacting bodies in (m) Replacing in [1] the expression of the force from [2] we get [3] 2 2 2 d GM a d GM m d m GM m F a Earth Earth Earth you you Earth you Earth = = / / = = Replacing the variables in [3] by their values G = 6.67x10-11 (N . m 2 /kg 2 ) M Earth = 5.97x1024 ( kg) m you ~ (200lb/2)~100 (kg)
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Unformatted text preview: d = 6400 (km) = 6400x1000 (m)=6.4x10 6 m 2 6 24 2 2 11 2 / 8 . 7 ) 10 4 . 6 ( ) 10 97 . 5 ( ) / 10 67 . 6 ( s m a m kg kg Nm d GM a Earth Earth Earth 2245 × × × × = =-b) F = m Earth x a you Newton’s second law of motion with F the force between the interacting pair in (N) m Earth , the Earth mass in (kg) a you , the acceleration due to your mass in (m/s 2 ) ] 4 [ Earth you you Earth you Earth Earth you Earth M F a a M a M M F a M F = = / × / = → × = On the other hand as before [5] 2 d m GM F you Earth = With F the force between the interacting pair in (N) M Earth the mass of the Earthg in (kg) m you , your mass in (kg) d the distance between the interacting bodies in (m) Replacing in [4] the expression of the force from [5] we get 2 2 22 6 2 2 11 2 / 016 0000000000 0000000000 . / 10 6 . 1 ) 10 4 . 6 ( ) 100 ( ) / 10 67 . 6 ( s m a s m a m kg kg Nm d GM a you you you you = × = × × × = =--...
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  • Fall '09
  • HUANG
  • kg, GM Earth

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