If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out. This happens
1 answer:
Answer:
True
Explanation:
If we swing a bucket of water fast enough in a vertical circle the water does not spill out even at the top-most position of the bucket. This happens because the centrifugal force acting away from the center in a circular motion neutralizes or overcomes the gravitational force on the water particles.
<u>Centrifugal force is mathematically related as:</u>
where:
m = mass of the revolving body
r = radius of revolution
angular velocity in radians per second
This force F acts in radially outward direction.
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1)
2) 13.9 s
Explanation:
1)
The acceleration due to gravity is the acceleration that an object in free fall (acted upon the force of gravity only) would have.
It can be calculated using the equation:
(1)
where
G is the gravitational constant
is the Earth's mass
r is the distance of the object from the Earth's center
The pendulum in the problem is at an altitude of 3 times the radius of the Earth (R), so its distance from the Earth's center is
where
is the Earth's radius
Therefore, we can calculate the acceleration due to gravity at that height using eq.(1):
2)
The period of a simple pendulum is the time the pendulum takes to complete one oscillation. It is given by the formula
where
L is the length of the pendulum
g is the acceleration due to gravity at the location of the pendulum
Note that the period of a pendulum does not depend on its mass.
For the pendulum in this problem, we have:
L = 3 m is its length
is the acceleration due to gravity (calculated in part 1)
Therefore, the period of the pendulum is: