Tension question

Question

A block of weight 38.4 N is hanging from a rope. The tension from the rope is pulling upward on the block. The block is accelerating upward at a rate of 1.70 m/s². What is the magnitude of the tension in the rope?

Answer 1

If this block were just hanging still, the Tension would be exactly equal to the weight of block (which is the same as F_g). So we know that the tension must be greater than 38.4 N for the block to accelerate upwards. That is, the net force on the block must be upwards.

The plan:

1. I always start with a free-body diagram, just including F_g and T.
2. From this, we can say that the magnitude of F_net = T - F_g. We already know that the direction of F_net must be upwards, since the acceleration is upwards.
3. Find the mass of the block using F_g = m * g, where g = 9.81 m/s², and F_g is given as the weight of the block, 38.4 N.
4. Use F_net = m*a to solve for the net force.
5. Now go back to what we wrote before: F_net = T - F_g and solve for T.
6. Remember to check that your answer makes sense -- it should be greater than 38.4 N, but not too much greater. I'd expect an answer in the high 40's.