A box with a mass of 20 kg is being lifted by a rope?

Question

Im not sure how to do these, any help? Thanks

a) sketch the situation and draw all the forces on the box.

I have 3 forces for this, is that all their is? I have one going up that the rope is putting on the box, and one that the box is putting on the rope, and then one that the gravity is putting on the box.

b) In 1.5s the box goes from rest to 2.5 m/s What is the magnitude of the tension in the rope? Is it greater than or less than the weight of the box?

I think I use v=vo+at to get this and find acceleration which is 1.667 m/s but I dont know how to write the answer...
c) The box then travels upward at a uniform velocity of 2.5 m/s. What is the Tension in the rope during this time? Is this greater than or less than the weight of the box?

d) The box then slows back to rest in just 0.50 s. What is the Tension in the rope during this time? Is this greater or less than the weight of the box?

Answer 1

a) The forces on the box are just your 1st and 3rd.

b) The q doesn't say whether it's going up or down. Makes a difference. I'll assume up.

You can calculate the net force using this acceleration (you should call it 1.7 considering 2 significant digits in the given info) and F=ma. The forces on the box are its weight and the tension. The net force is the resultant of these 2. So the tension is larger than the weight by the amount of net force.

c) The box is not under acceleration, therefore there is no net force. The rope needs only support the weight.

d) Again use v=vo+at. And then calculate the net force. The net force is the difference between tension and weight. In this case the weight is larger than the tension.

Answer 2

b) The max tension is 20 (9.8 + 2.5/1.5) = 229.3 N (>box)
c) 20*9.8 (=box)
d) 20*(9.8-2.5/.5) = 96N (