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)