what will be the effect on the acceleration due to gravity of the earth if it is compressed to a the size the moon?
2 answers:
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Answer:
Explanation:
We have an uniform circular motion, therefore, the pebble’s speed is given by the distance traveled in a revolution and the period (T), since this is the time pebble’s takes to complete a revolution:
The period is inversely proportional to the frequency:
So, we have:
Recall that the radius is the half of the diameter and one revolution per is equal to one Hz:
The centripetal acceleration is defined as:
A) +5 J
B) +1 J
Explanation:
A)
The internal forces (interaction forces) acting on a system do not change the mechanical energy (sum of potential and kinetic energy) of the system.
However, these forces are responsible for converting the energy from one form into another; the work done by these forces is equal to the amount of energy converted from one form into the other.
In this problem, we have:
is the loss in potential energy of the system
is the gain in kinetic energy of the system
By looking at these numbers, this means that the internal forces have converted 5 J of energy from potential energy into kinetic energy (while the additional +1 J missing is due to external forces, as explained in part B).
Therefore, the work done by internal forces is
W = +5 J
B)
First of all, we calculate the change in mechanical energy of the system.
The mechanical energy of a system is the sum of its kinetic energy (K) and its potential energy (U):
So, the change in mechanical energy is equal to the sum of the changes of kinetic energy and the changes of potential energy:
In this problem:
So, the change in mechanical energy is:
According to the work-energy theorem, the work done by external forces on a system is equal to the change in mechanical energy of the system: therefore in this case, the work done by external forces is