Answer
The tension is the same whether the crate is hanging at rest or moving upward at constant velocity. If the crate is traveling upward, the tension in the string is greater when the crate is speeding up than when it is slowing down.
Work Step by Step
The tension is the same whether the crate is hanging at rest or moving upward at constant velocity. The tension in the string is just equal to the weight, because in both cases the velocity is constant. Newton’s first law tells us that the net force on the object is zero.
If the crate is traveling upward, the tension in the string is greater when the crate is speeding up than when it is slowing down. The upwardly-directed tension in the string is greater than the weight when it is speeding up, because the acceleration is upward, and Newton’s second law tells us that the net force on the object is upward.
If the crate is moving upward and slowing down, the acceleration is downward, and the tension is less than the weight.
