Can anyone please help me with the following problem?


Each of the weights A and B has a mass M and C has a mass of kM.

A) If the system is released form rest find the acceleration of the moveable pulley and the scale pan and show that the scale pan will ascend if k > 4.

B) When the system is moving freely find the tension in the string.

It is part B that is confusing me. In fact I don't need to solve part A to solve part B, but whether I use my answer from part A or not I get the same answer for part B which is different from the text book answer.

Here's my solution for part A:

I set the acceleration of the pan to a in a downwards direction.

Then the acceleration of C in the upward direction will be a/2, as the string to the left of C is not accelerating and the string to the right of C is accelerating at a.

For C:


For pan:


Now I do the algebra to eliminate T and arrive at:


Great, if k > 4 then a is negative and so pan ascends - as was to be shown.

For part B I could substitute my value of a into one of the original two equations, or simply eliminate a from those original two equations.

Doing the latter:




This leads to:


But the book answer is:


Which is not even close to mine.

  • $\begingroup$ You might want to look at the units of your answer versus those of the book's answer. What units do you expect $T$ to have? $\endgroup$
    – John Hughes
    Apr 17, 2018 at 19:15

1 Answer 1


Since C has mass $km$ your equation of motion for C should be


instead of


And your equation of motion for the pan should be


instead of


  • $\begingroup$ Thanks so much. Stupid mistakes as ever, was looking right through them every time. Thanks again, Mitch. $\endgroup$ Apr 17, 2018 at 13:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.