Find the attachment for solution
Help
A is the Helmholtz free energy. It's derivative with respect to temperature(not time), gives the entropy, S
Answers:
a)
b)
Explanation:
a) Accoding to the Universal Law of Gravitation we have:
(1)
Where:
is the gravitational force between the eagle and the throng
is the Universal Gravitational constant
is the mass of the eagle
is the mass of the throng
is the distance between the throng and the eagle
(2)
(3) As we can see the gravitational force between the eagle and the throng is quite small.
b) The attraction force between the eagle and Earth is the weight of the eagle, which is given by:
(4)
Where is the acceleration due gravity on Earth
(5)
(6)
Now we can find the ratio between and :
As we can see this ratio is also quite small
(a) 907.5 N/m
The force applied to the spring is equal to the weight of the object suspended on it, so:
The spring obeys Hook's law:
where k is the spring constant and is the stretching of the spring. Since we know , we can re-arrange the equation to find the spring constant:
(b) 1.45 cm
In this second case, the force applied to the spring will be different, since the weight of the new object is different:
So, by applying Hook's law again, we can find the new stretching of the spring (using the value of the spring constant that we found in the previous part):
(c) 3.5 J
The amount of work that must be done to stretch the string by a distance is equal to the elastic potential energy stored by the spring, given by:
Substituting k=907.5 N/m and , we find the amount of work that must be done:
D is definitely the correct choice here.
I think a case could also be made for choice-B, but that would be a tough, complex operation.