Problem Statement:
"On the planet Newtonia, a simple pendulum having a bob with mass 1.05kg and a length of 170.0cm takes 1.43s , when released from rest, to swing through an angle of 12.5 ∘, where it again has zero speed. The circumference of Newtonia is measured to be 51400 km."
Question: "What is the mass of the planet Newtonia?"
No matter what I do, I always end up getting 3.24995 * 10 ^26 as my answer. :( Please help.
"On the planet Newtonia, a simple pendulum having a bob with mass 1.05kg and a length of 170.0cm takes 1.43s , when released from rest, to swing through an angle of 12.5 ∘, where it again has zero speed. The circumference of Newtonia is measured to be 51400 km."
Question: "What is the mass of the planet Newtonia?"
No matter what I do, I always end up getting 3.24995 * 10 ^26 as my answer. :( Please help.
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It is swinging from one side to the other. That's half a period. So the period is 2*1.43 = 2.86 seconds.
Ah, I see where you went wrong, because at first I got the same number you did.
51400 km = 5.14 x 10^7 meters is not the radius. It's the circumference. The radius is 5.14 x 10^7/(2 pi) = 8.18 x 10^6 m.
Ah, I see where you went wrong, because at first I got the same number you did.
51400 km = 5.14 x 10^7 meters is not the radius. It's the circumference. The radius is 5.14 x 10^7/(2 pi) = 8.18 x 10^6 m.
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T = 1.43 s
T ≃ 2π√(L/gᵩ) where L = 170.0 cm = 0.1700 m and gᵩ = Gmᵩ/rᵩ² mᵩ,rᵩ are mass & radius of planet Newtonia
So, I assume your problem is an inability to use a calculator?
T² ≃ 4π²L/gᵩ, gᵩ ≃ 4π²L/T²
gᵩ = Gmᵩ/rᵩ² ≃ 4π²L/T² ; mᵩ≃ 4π²Lrᵩ²/(GT²) = (2πrᵩ/T)² L ÷ G
G = 6.67384E-11 Nm²/kg²
rᵩ = 51 400 000 m
T = 1.43*2 s
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I get 3.25E25 kg
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I would immediately fail anyone who reported a result to more than 4 significant figures.
T ≃ 2π√(L/gᵩ) where L = 170.0 cm = 0.1700 m and gᵩ = Gmᵩ/rᵩ² mᵩ,rᵩ are mass & radius of planet Newtonia
So, I assume your problem is an inability to use a calculator?
T² ≃ 4π²L/gᵩ, gᵩ ≃ 4π²L/T²
gᵩ = Gmᵩ/rᵩ² ≃ 4π²L/T² ; mᵩ≃ 4π²Lrᵩ²/(GT²) = (2πrᵩ/T)² L ÷ G
G = 6.67384E-11 Nm²/kg²
rᵩ = 51 400 000 m
T = 1.43*2 s
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I get 3.25E25 kg
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I would immediately fail anyone who reported a result to more than 4 significant figures.
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3.24995*12^28