Suppose that F is an inverse square force field, that is, cr F(r) = |r|³ for some constant c, where r = xi + yj + zk. (a) Find the work done by F in moving an object from a point P₁ along a path to a point P₂ in terms of the distances d₂ and d₂ from these points to the origin. (b) An example of an inverse square field is the gravitational field -(mMG) r |r1³ F = Use part (a) to find the work done (in J) by the gravitational field when the earth moves from aphelion (at a maximum distance of 1.52 x 108 km from the sun) to perihelion (at a minimum distance of 1.47 x 108 km). Use the values m = 5.97 x 1024 kg, M = 1.99 x 1030 kg, and G = 6.67 x 10-¹1 N. m²/kg2. (Round your decimal part to two decimal places.) x 1032 J (c) Another example of an inverse square field is the electric force field EqQr |r³ F = Suppose that an electron with a charge of -1.6 x 10-19 C is located at the origin. A positive unit charge (1 C) is positioned a distance 10-12 m from the electron and moves to a position half that distance from the electron. Use part (a) to find the work done (in J) by the electric force field. (Use the value = 8.985 x 10°. Round your answer to the nearest hundred joules.) J
Suppose that F is an inverse square force field, that is, cr F(r) = |r|³ for some constant c, where r = xi + yj + zk. (a) Find the work done by F in moving an object from a point P₁ along a path to a point P₂ in terms of the distances d₂ and d₂ from these points to the origin. (b) An example of an inverse square field is the gravitational field -(mMG) r |r1³ F = Use part (a) to find the work done (in J) by the gravitational field when the earth moves from aphelion (at a maximum distance of 1.52 x 108 km from the sun) to perihelion (at a minimum distance of 1.47 x 108 km). Use the values m = 5.97 x 1024 kg, M = 1.99 x 1030 kg, and G = 6.67 x 10-¹1 N. m²/kg2. (Round your decimal part to two decimal places.) x 1032 J (c) Another example of an inverse square field is the electric force field EqQr |r³ F = Suppose that an electron with a charge of -1.6 x 10-19 C is located at the origin. A positive unit charge (1 C) is positioned a distance 10-12 m from the electron and moves to a position half that distance from the electron. Use part (a) to find the work done (in J) by the electric force field. (Use the value = 8.985 x 10°. Round your answer to the nearest hundred joules.) J
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Transcribed Image Text:Suppose that F is an inverse square force field, that is,
F(r) =
cr
for some constant c, where r = xi + yj + zk.
(a) Find the work done by F in moving an object from a point P₁ along a path to a point P₂ in terms of the distances d₁ and d₂ from these points to the origin.
F =
|r|³
(b) An example of an inverse square field is the gravitational field
-(mMG) r
F =
|r|³
Use part (a) to find the work done (in J) by the gravitational field when the earth moves from aphelion (at a maximum distance of 1.52 x 108 km from the sun) to perihelion (at a minimum distance of
1.47 x 108 km). Use the values m = 5.97 x 1024 kg, M = 1.99 x 10³0 kg, and G = 6.67 × 10-¹¹ N·m²/kg². (Round your decimal part to two decimal places.)
x 1032 J
(c) Another example of an inverse square field is the electric force field
EqQr
|r|³
Suppose that an electron with a charge of -1.6 × 10-19 C is located at the origin. A positive unit charge (1 C) is positioned a distance 10-¹2 m from the electron and moves to a position half that distance from the
electron. Use part (a) to find the work done (in J) by the electric force field. (Use the value = 8.985 × 10⁹. Round your answer to the nearest hundred joules.)
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