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Problem 9: The weight of a person of mass m = 132 kg as measured at sea level is equal to W₁ and at the top of the Vinson Massif (the highest peak in Antarctica) is W₂. Determine the weight difference ΔW = W₁ - W₂. Hint: The product GM = 3.99x10¹⁴ Nm²/kg, the radius of the Earth Rₑ = 6.38×10⁶ m, and the height h above sea level of the Vinson Massif is equal to 5.14×10³ m.

          Problem 9: The weight of a person of mass m = 132 kg as measured at sea level is equal to W₁ and at the top of the Vinson Massif (the highest peak in Antarctica) is W₂. Determine the weight difference ΔW = W₁ - W₂. Hint: The product GM = 3.99x10¹⁴ Nm²/kg, the radius of the Earth Rₑ = 6.38×10⁶ m, and the height h above sea level of the Vinson Massif is equal to 5.14×10³ m.
        
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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Problem 9: The weight of a person of mass m = 132 kg as measured at sea level is equal to W₁ and at the top of the Vinson Massif (the highest peak in Antarctica) is W₂. Determine the weight difference ΔW = W₁ - W₂. Hint: The product GM = 3.99x10¹⁴ Nm²/kg, the radius of the Earth Rₑ = 6.38×10⁶ m, and the height h above sea level of the Vinson Massif is equal to 5.14×10³ m.
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Transcript

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00:01 We're probably, there's a climber who has a mass of 70 kilograms, but unfortunately they kind of screw up mass and weight.
00:13 So let's see, did they say the mass of the earth? this forces, suppose a person weighs, yeah, weighs 70 kilograms at sea level.
00:23 That's not their weight, that's their mass.
00:27 Although, you know, that's a common, commonly basically take a factor of g out when we measure weight.
00:34 So this is really, this is really a mass.
00:38 And we say that they have this mass at sea level, and then they climb up to the top of mount everest, and when they ask, well, their mass doesn't change.
00:47 So you would say, well, if this is really the weight, then their weight doesn't change.
00:51 But that's because the weight is actually in newton's.
00:55 And so if you worked out the units on this you would not get kilograms get newtons and so there's kind of a disconnect between the physics and the math here i wish the math people would worry a little more about getting the physics right but anyway so we can look at this you know change in in distance from the center of the earth as a as a delta problem so we can take assuming these things are a constant dw equals minus minus 2g, capital m, lowercase m, all over r cubed, d .r.
01:30 So then delta w is roughly delta this constant times delta r...
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