Two blocks with masses M1 and M2 hang one under the other.
For this problem, take the positive direction to be upward, and use g for the magnitude of the acceleration due to gravity.
Blocks at rest For Parts (a) and (b) assume the blocks are at rest.
(a) Find T2, the tension in the lower rope. Express your answer in terms of some or all of the variables M1, M2, and g.
(b) Find T1, the tension in the upper rope. Express your answer in terms of some or all of the variables M1, M2, and g.
For Parts (c) and (d) the blocks are now accelerating upward (due to the tension in the strings) with an acceleration of magnitude a.
(c) Find T2, the tension in the lower rope. Express your answer in terms of some or all of the variables M1, M2, and g.
(d) Find T1, the tension in the upper rope. Express your answer in terms of some or all of the variablesM1, M2, a and g.

(a)T= M2 × g,    (b)T= (M1 + M2)g,   (c)T= M2 (a + g) and  (d)T=(M1 + M2) (a + g)

Explanation:

M1 is hanged upper and M2 is lower at Rest.

(a) For M2

T2 = Weight of the Body M2= M2 × g

(b) T1 = Weight of the Body M2 + Weight of the Body M2

T1 = M1 g + M2 g = (M1 + M2)g

M1 is hanged upper and M2 is lower at accelerated upwards ( F = T - W)

(c) For M2

⇒T = M2a + M2g = M2 (a + g)

(d) For M1

T = (M1 + M2) a + (M1 + M2) g

⇒ T = (M1 + M2) (a + g)

the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day