6
$\begingroup$

I want some intuitive understanding on why there will be a range in tension in the below question. (On solving we will get that the system is at rest ($a=0$) and since its starts from rest the blocks will be stationary). Now, this seems experimentally feasible to have a unique absolute tension and I wonder why this is not the case (I initially thought friction might change but as the blocks are stationary it's not the case).

A system of two blocks and a light string are kept on two inclined faces (rough) as shown in the figure below. All the required data are mentioned in the diagram. Pulley is light and frictionless. (Take $g=10\,\text m/\text s^2$, $\sin37^\circ=3/5$) If the system is released from rest then what is the range of the tension in the string?

enter image description here

Note: Please assume the wedge to be at rest even though not mentioned.

Improve this question
$\endgroup$

3 Answers 3

Reset to default
7
$\begingroup$

I initially thought friction might change but as the blocks are stationary it's not the case

It's not that friction is changing over time, it's that the specific value for friction (in the static case) is unknown, so the specific value for tension is also unknown. You know the maximum possible value for static friction on the blocks, but not the specific value.

Let's go to a more extreme case. Imagine that the coefficient of friction is so high that the blocks can remain in place on the ramp without a rope. When you set them down, what is the tension on the rope? The answer is that it depends. You could put them down with 0 tension and they would stay in place. You could put them down with very high tension and they would stay in place.

For the problem given, the low coefficient of friction limits the possible values for tension, but doesn't indicate a unique value.

Improve this answer
$\endgroup$
0
6
$\begingroup$

A simpler example may illustrate why a range of tensions is possible when friction is involved.

A horizontal string is attached to a block of mass $m$ which rests on a horizontal plane. The coefficient of friction between the block and the plane is $\mu$. If the block is at rest the tension in the string may take any value between $0$ and $\mu mg$.

Improve this answer
$\endgroup$
1
  • 1
    $\begingroup$ @shriram It was not a stupid question and it may help others, so I would recommend not deleting it. $\endgroup$
    – gandalf61
    Commented Aug 6, 2021 at 17:16
-1
$\begingroup$

It appears to me that the static friction forces are not sufficient to hold the blocks in place. The 10 kg will slide down and drag the 5 kg up. If the string stretches a bit, there may be a brief maximum tension before the 5 kg starts up.

Improve this answer
$\endgroup$
2
  • $\begingroup$ Net force parallel to the plane due to gravity and normal forces is less than the maximum possible static friction. It is possible to remain at rest. $\endgroup$
    – Bill N
    Commented Aug 7, 2021 at 15:24
  • $\begingroup$ Bill N: You are right. Maybe the range depends on which friction force is at its maximum. $\endgroup$
    – R.W. Bird
    Commented Aug 7, 2021 at 19:35

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