Man A (70kg) and Man B (90kg) are hanging motionless from a platform at rest. What is the tension TA in the top rope if the platform accelerates upward at a constant rate of 2 m/s2

The tension in the upper rope (top rope), T1 = 1,888 N

Explanation:

The Parameters that were given:

Mass A, M1 = 70kg

Mass B. M2 = 90kg

acceleration, a = 2 m/s2

Assume the rope doesn't have mass, acceleration due to gravity, g

= 9.8 m/s2

The tension, T in a platform = m (a + g)

Then the tension, T1 in the upper rope = m1 (a + g) + T2

Where T2 = Tension in the lower rope

First, we calculate T2

Since the platform accelerates upward the acceleration would be positive

T2 =  m2 (a + g)

T2 = 90kg ( 2 m/s2 + 9.8 m/s2)

T2 = 1,062N

To calculate the tension T1,

T1 = m1 (a + g) + T2

= 70kg (2 m/s2 + 9.8 m/s2) + 1062N

T1 = 1,888 N