I am struggling with the following question, which is one of the questions in a book for one of the papers for Cambridge International AS and A Level Mathematics - "Mechanics 1" (Even though this is one of Mathematics papers, it is also pretty much related to Physics):
A load of 7000 Newtons is being raised from rest with constant acceleration by a cable. After the load has been raised 20 metres, the cable suddenly becomes slack. The load continues upwards for a distance of 4 metres before coming to instantaneous rest. Assuming no air resistance, find the tention in the cable before it became slack. (In this question, acceleration due to gravity "g" is 10 ms^(-2))
I am not sure how to interpret a part of this question highlighted in red above, but my approach to work out this question would be like this:
Weight of a load (W) = g X Mass, so 7000 = 10 X Mass, therefore, Mass of the load is 700 kg.
Net force = Tension (T) - Weight (W) = Tension - 7000
Also,
Net force = acceleration (a) X Mass of the load = 700a
So Tension - 7000 = 700a
So Tension = 700a + 7000
But how can we find the acceleration (a) in this context?
If you draw a veolocity - time graph, the line would start from the origin (0, 0) with a gradient equal to "a" up to a certain time where the area of the triangle beween the line and t-axis is 20. Then the gradient "a" will be smaller because the cable becomes slack and then the velocity drops all of a sudden to 0 because the question says "...coming to instantaneous rest". So I would imagine the graph would look like "Diagram 1" (or Scenario 1) indicated on the attachment here. Am I correct?
However, then how can we possibly determine the acceleration because we are not given any information about time or velocity?
I would much appreciate it if someone can help me with this question.
Thank you.
P.S. By the way, the answer section in the book says that the correct answer to this question is 8400N, which means that "a = 2" because 8400 - 7000 = 700 X 2
