I would carry a 25 pound box up 5 flights, because it is lighter. You will wear out faster carrying a 50 pound box up 3 flights.
Answer:
G M m / R^2 = m v^2 / R gravitational force = centripetal force
G M = v^2 R = constant
As v increases R will must decrease
Take the moon as an example
S = 2 pi R where R is about 240,000 miles for one orbit
S / 1 day = 54,000 miles/day for a 28 day circuit
S / 1 hr = 54000 / 24 = 2200 mph which is much less than a satellite in orbit
(a) Let 
be the maximum linear speed with which the ball can move in a circle without breaking the cord. Its centripetal/radial acceleration has magnitude
where 
is the radius of the circle.
The tension in the cord is what makes the ball move in its plane. By Newton's second law, the maximum net force on it is
so that
Solve for :
(b) The net force equation in part (a) leads us to the relation
so that is directly proportional to the square root of . As the radius increases, the maximum linear speed will also increase, so the cord is less likely to break if we keep up the same speed.
