Answer:
T = 99.51 hour
Explanation:
Mass of Uranus,
The moon Umbriel orbits Uranus at a distance of
We need to find Umbriel's orbital period. Let it is T. Using Kepler's third law of motion to find it.
As 1 hour = 3600 s
358244.51 s = 99.51 hour
Hence, Umbriel's orbital period is 99.51 hour.
Hi there!
(a)
Recall that:
W = Work (J)
F = Force (N)
d = Displacement (m)
Since this is a dot product, we only use the component of force that is IN the direction of the displacement. We can use the horizontal component of the given force to solve for the work.
To the nearest multiple of ten:
(b)
The object is not being displaced vertically. Since the displacement (horizontal) is perpendicular to the force of gravity (vertical), cos(90°) = 0, and there is NO work done by gravity.
Thus:
(c)
Similarly, the normal force is perpendicular to the displacement, so:
(d)
Recall that the force of kinetic friction is given by:
Since the force of friction resists the applied force (assigned the positive direction), the work due to friction is NEGATIVE because energy is being LOST. Thus:
In multiples of ten:
(e)
Simply add up the above values of work to find the net work.
Nearest multiple of ten:
(f)
Similarly, we can use a summation of forces in the HORIZONTAL direction. (cosine of the applied force)
Nearest multiple of ten: