- #1
Selim Bradley
- 12
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Hello everyone! Please, help me understand the following problem:
Earth's orbit around the Sun is nearly circular. The period is 1 yr = 365.25 d.
(a) In an elapsed time of 5 d, what is Earth's angular displacement? Solved!
(b) What is the change in Earth's velocity, Δv? Confused!
ω = Δθ/Δt
v = rω
I easily solved the first problem doing this: Δθ = (2π x 5 days)/365.25 days = 0.0860 rads
However, whenever I enter a solution for the second problem, the computer does not accept my answer, even though I'm solving it correctly. This is what I did:
First, I tried to solve for the angular velocity of the object. Since the computer wants the answer in meters per second, I converted Δt to seconds:
ω = Δθ/Δt = 0.0860121192 rads / (5 days x 86,400 sec) = 1.99x10^-7 rads/sec
Now, I substitute the distance between the sun and the Earth in meters and the angular velocity into v = rω to solve for v.
v = rω = (1.5x10^14 m)(1.99x10^-7 rads/sec) = 2.99x10^7 m/s
The correct answer, according to the computer, should be 2570 m/s.
What am I doing wrong?
Homework Statement
Earth's orbit around the Sun is nearly circular. The period is 1 yr = 365.25 d.
(a) In an elapsed time of 5 d, what is Earth's angular displacement? Solved!
(b) What is the change in Earth's velocity, Δv? Confused!
Homework Equations
ω = Δθ/Δt
v = rω
The Attempt at a Solution
I easily solved the first problem doing this: Δθ = (2π x 5 days)/365.25 days = 0.0860 rads
However, whenever I enter a solution for the second problem, the computer does not accept my answer, even though I'm solving it correctly. This is what I did:
First, I tried to solve for the angular velocity of the object. Since the computer wants the answer in meters per second, I converted Δt to seconds:
ω = Δθ/Δt = 0.0860121192 rads / (5 days x 86,400 sec) = 1.99x10^-7 rads/sec
Now, I substitute the distance between the sun and the Earth in meters and the angular velocity into v = rω to solve for v.
v = rω = (1.5x10^14 m)(1.99x10^-7 rads/sec) = 2.99x10^7 m/s
The correct answer, according to the computer, should be 2570 m/s.
What am I doing wrong?
. However, before telling my professor, it would be nice if someone in the Physics Forums could check my work and OK it first, if that's alright. 