Acceleration directed toward the center of a circular path that produces uniform circular motion is
2 answers:
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We can use the law of conservation of energy to solve the problem.
The total mechanical energy of the system at any moment of the motion is:
where U is the potential energy and K the kinetic energy.
At the beginning of the motion, the ball starts from the ground so its altitude is h=0 and therefore its potential energy U is zero. So, the mechanical energy is just kinetic energy:
When the ball reaches the maximum altitude of its flight, it starts to go down again, so its speed at that moment is zero: v=0. So, its kinetic energy at the top is zero. So the total mechanical energy is just potential energy:
But the mechanical energy must be conserved, Ef=Ei, so we have
and so, the potential energy at the top of the flight is
The total mechanical energy of the system at any moment of the motion is:
where U is the potential energy and K the kinetic energy.
At the beginning of the motion, the ball starts from the ground so its altitude is h=0 and therefore its potential energy U is zero. So, the mechanical energy is just kinetic energy:
When the ball reaches the maximum altitude of its flight, it starts to go down again, so its speed at that moment is zero: v=0. So, its kinetic energy at the top is zero. So the total mechanical energy is just potential energy:
But the mechanical energy must be conserved, Ef=Ei, so we have
and so, the potential energy at the top of the flight is
Case d) has the strongest gravitational force
Explanation:
The magnitude of the gravitational force between two objects is given by the equation:
where :
is the gravitational constant
m1, m2 are the masses of the two objects
r is the separation between the objects
a) For this pair of objects:
m1 = 10 kg
m2 = 2 kg
r = 30 km = 30,000 m
So the gravitational force is
b) For this pair of objects:
m1 = 10 kg
m2 = 10 kg
r = 30 km = 30,000 m
So the gravitational force is
c) For this pair of objects:
m1 = 2 kg
m2 = 2 kg
r = 10 km = 10,000 m
So the gravitational force is
d) For this pair of objects:
m1 = 10 kg
m2 = 10 kg
r = 10 km = 10,000 m
So the gravitational force is
Therefore, the strongest gravitational force is in case d).
Learn more about gravitational force:
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