What is the source of gentian viole?
1 answer:
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1. 0.16 N
The weight of a man on the surface of asteroid is equal to the gravitational force exerted on the man:
where
G is the gravitational constant
is the mass of the asteroid
m = 100 kg is the mass of the man
r = 2.0 km = 2000 m is the distance of the man from the centre of the asteroid
Substituting, we find
2. 1.7 m/s
In order to stay in orbit just above the surface of the asteroid (so, at a distance r=2000 m from its centre), the gravitational force must be equal to the centripetal force
where v is the minimum speed required to stay in orbit.
Re-arranging the equation and solving for v, we find:
We can solve the problem by applying Newton's second law, which states that the resultant of the forces acting on an object is equal to the product between its mass and its acceleration:
We should consider two different directions: the direction perpendicular to the inclined plane and the direction parallel to it. Let's write the equations of the forces along the two directions, decomposing the weight of the object (mg):
(parallel direction) (1)
(perpendicular direction) (2)
where
is the angle of the inclined plane, N is the normal reaction of the plane, 
is the frictional force, with 
being the coefficient of friction.
From eq.(2), we find
and if we substitute into eq.(1), we can find the acceleration of the block:
from which
We should consider two different directions: the direction perpendicular to the inclined plane and the direction parallel to it. Let's write the equations of the forces along the two directions, decomposing the weight of the object (mg):
where
From eq.(2), we find
and if we substitute into eq.(1), we can find the acceleration of the block:
from which