suspending two blocks connected by a string of negligible mass over a pulley. the blocks are initially held at rest and then released at time t = 0 find the speed of the block at t = 4?

v = (m₁ - m₂) / (m₁ + m₂) 39.2

Explanation:

For this exercise, let's use Newton's second law, since the mass of the chain is zero has forces. Let's call the block on the left 1 and the one on the right 2

For the block on the left

W₁ - T = m₁ a

For the block on the right

T - W₂ = m₂ a

Where the acceleration (a) is the same for the entire system, so that the chain does not lose tension,

To solve this system of equations let's add it

W₁ - W₂ = (m₁ + m₂) a

a = (m₁ - m₂) / (m₁ + m₂) g

Now we can use the kinematic relationship to find the speed of the block

v = v₀ + a t

v = 0 + (m₁ - m₂) / (m₁ + m₂) g t

We substitute the time t = 4 s

v = (m₁ - m₂) / (m₁ + m₂) 9.8 4

v = (m₁ - m₂) / (m₁ + m₂) 39.2

For a specific value we must have the mass of the blocks