The cat righting reflex is a cat's innate ability to orient itself as it falls in order to land on its feet. The righting reflex
begins to appear at 3–4 weeks of age, and is perfected at 7 weeks. The minimum height required for this to occur in most cats would be around 30 cm. You are part of an engineering team trying to reproduce this in a mechanical cat. Your prototype, aptly named Katt, when dropped motionless, upside down from 2.5 m, can right itself before it hits the ground by rotating its "tail". Katt’s body is a solid cylinder 30 cm in length and 15 cm in diameter, with a mass of 3.0 kg. Attached to the center of one end of the body is Katt's tail, a 20-cm long rod which extends out perpendicular to Katt's body and has only 10% the mass of the body. The tail will rotate due to a small electric motor in the body that produces a constant torque. In order to order the piece, determine the angular speeds it will need to deal with.
1 answer:
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Answer: 6,400 km
Explanation:
The weight of a person is given by:
where m is the mass of the person and g is the acceleration due to gravity. While the mass does not depend on the height above the surface, the value of g does, following the formula:
where
G is the gravitational constant
M is the Earth's mass
r is the distance of the person from the Earth's center
The problem says that the person weighs 800 N at the Earth's surface, so when r=R (Earth's radius):
(1)
Now we want to find the height h above the surface at which the weight of the man is 200 N:
(2)
If we divide eq.(1) by eq.(2), we get
By solving the equation, we find:
which has two solutions:
--> negative solution, we can ignore it
--> this is our solution
Since the Earth's radius is , the person should be at
above Earth's surface.
Answer:
132.9 cm
Explanation:
Data provided in the question:
Radius of the basll = 76 cm = 0.76 m
Side of the box = 200 cm = 2 m
Density of the ball and cube are equal
let the density be 'D'
Now,
Mass of ball, M = Volume × Density
= × D
= × D
= 1.838D
Mass of cube, m = L³ × D
= 2³ × D
= 8D
Thus,
center of mass, y = [ My₁ + my₂ ] ÷ [M + m]
here,
y₁ = center of mass of ball with respect to floor
as the center mass of sphere lies at the center of the sphere
= Length of cube + radius of sphere
= 2 + 0.76
= 2.76 m
y₂ = Center of mass of cube = = 1 m
Thus,
y = [ ( 1.838D × 2.76 ) + (8D × 1 ) ] ÷ [1.838D + 8D]
= 13.07288D ÷ 9.838D
= 1.329 m
or
= 132.9 cm