Question

p2
Q3: In an Atwood machine, the Hamiltonian is given as, H (X,P) = + (M2-M)gX, where symbols have
2(M, +M2)
their usual meanings. Find out [[X, H), H).
​

Answer 1

Answer:

Before the sting becomes taut, let the acceleration of the blocks be a

We have then,

2mg−mg=(2m+m)a

⇒mg=3ma⇒a=

3

g

Now,

3

g

is the acceleration of the 2m and m until the string becomes taut.

Using

v

2

−u

2

=2as, we have

u=0

We know the 2m mass falls a distance x before the limp string becomes taut.

⇒v

2

=2

3

g

x

⇒v=

3

2gx

Now a sudden impulsive force T

l

due to the tension developed in the limp string acts on the remaining systems for dt time.

Given, after the string becomes taut, the masses on the left rise at the same speed. Let the speed be c.

From Impulse momentum theorem, we know that Impulse is equal to change in momentum

J=Fdt=Δmv

Applying this theorem for all the three blocks, we have

(half answer this is first and you continue next with the attachment)

Explanation:

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