Question

Two blocks with masses M1 and M2 hang one under the other.

Answer 1

Answer:

a. T2 = M2g

b. T1 = (M2 + M1)g

c. T2 = M2(g + a)

d. T1 = (M2 + M1)(g + a)

Explanation:

Given Parameters

- Two blocks with masses M1 and M2 hang one under the other.

- positive direction is represented by upward movement

Tension simply means the contact force exerted by a rope/spring when in contact with a body.

Tension is calculated by mass * acceleration

a. Finding T2, the tension in the lower rope (the body is at rest)

Here, the tension only act on the lower rope, hence only the second body is affected by this tension.

Provided that the body is at rest, then only acceleration of gravity acts on this body

Using Tension = Mass * Acceleration

Where Tension = T2

Mass = M2

Acceleration = g

Then, we have

T2 = M2 * g

T2 = M2g

b. Finding T1, the tension in the upper rope (the body is at rest)

We use the same analysis as (a) above but here, the tension acts on the upper rope, hence both bodies are affected by this tension.

Provided that the body is at rest, then only acceleration of gravity acts on this body

Using Tension = Mass * Acceleration

Where Tension = T1

Mass = Summation of Both Masses = M2 + M1

Acceleration = g

Then, we have

T1 = (M1 + M2) * g

T1 = (M1 + M2)g

c. Finding T2, the tension in the lower rope (the body is in motion)

We use the same analysis as (c) above but here, the tension acts on the upper rope, hence both bodies are affected by this tension.

Provided that the body is in motion, then acceleration of gravity (g) and the body's acceleration (a) will be taken into consideration

Using Tension = Mass * Acceleration

Since, positive direction is represented by upward movement; we have

Tension = (Mass * Acceleration of gravity) + (Mass * Body's Acceleration)

Where Tension = T2

Mass = M2

Acceleration of gravity = g

Body's Acceleration = a

Then, we have

T2 = M2 * g + M2 * a

T2 = M2(g + a)

d. Finding T2, the tension in the lower rope (the body is in motion)

Here, the tension only act on the lower rope, hence only the second body is affected by this tension.

Provided that the body is in motion, then acceleration of gravity (g) and the body's acceleration will be taken into consideration

Using Tension = Mass * Acceleration

Since, positive direction is represented by upward movement; we have

Tension = (Mass * Acceleration of gravity) + (Mass * Body's Acceleration)

Where Tension = T2

Mass = M2 + M1

Acceleration of gravity = g

Body's Acceleration = a

Then, we have

T2 = (M2 + M1) * g + (M2 + M1) * a

T2 = (M2 + M1)(g + a)

Answer 2

Answer:

(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)