The moon Ariel orbits Uranus at a distance of 1.91 x 108 m once every 2.52 days. Use that data to calculate the mass of Uranus.
1 answer:
Mu = 8.66 × 10^25 kg
Explanation:
centripetal force = gravitational force
where
m = mass of moon Ariel
mu = mass of Uranus
r = radius of Ariel's orbit
v = Ariel's velocity around Uranus
To find the velocity, we need to find the circumference of the no orbit and then divide it by the period (2.52 days):
circumference = 2πr = 2π×(1.91 × 10^8 m)
= 1.2 × 10^9 m
period = 2.52 days × (24 h/1 day)×(3600 s/1 hr)
= 2.18 × 10^5 s
v = (1.2 × 10^9 m)/(2.18 × 10^5 s)
= 5.5 × 10^3 m/s
(5.5 × 10^3 m/s)^2/(1.91 × 10^8 m) = (6.67 × 10^-11 m^3/kg-s^2)Mu/(1.91 × 10^8 m)^2
Solving Mu,
Mu = 8.66 × 10^25 kg
You might be interested in
Explanation:
The given data is as follows.
Length of beam, (L) = 5.50 m
Weight of the beam, () = 332 N
Weight of the Suki, () = 505 N
After crossing the left support of the beam by the suki then at some overhang distance the beam starts o tip. And, this is the maximum distance we need to calculate. Therefore, at the left support we will set up the moment and equate it to zero.
= 0
x =
=
= 0.986 m
Hence, the suki can come (2 - 0.986) m = 1.014 from the end before the beam begins to tip.
Thus, we can conclude that suki can come 1.014 m close to the end before the beam begins to tip.
Answer:
Explanation:
given,
Angular speed of the tire = 32 rad/s
Displacement of the wheel = 3.5 rev
Δ θ = 3.5 x 2 π
= 7 π rad
now,
Time interval of the car to rotate 7π rad
using equation
Time taken to rotate 3.5 times is equal to 0.687 s.