<p>i got stuck on this problem</p>
<p>the force diagram is basically like this:</p>
<p>M and m
|B|-------> F</p>
<p>in which
M is the mass of a block and m is the mass of a rope attached on the block. F is the force pulling on the rope, the bottum is frictionless.</p>
<p>the question is what is the tenson in the rope at its midpoint</p>
<p>the answer is F(m + 2M) / 2(m + M)</p>
<p>but i dont get it</p>
<p>the following is my force diagram of rope</p>
<p>Ma +ma/2 <-------@------->F+ma/2</p>
<p>Also there should be a gravity comes out from @ like some thing below</p>
<p>@<br>
|
|
|
\/
mg</p>
<p>I dont get it</p>
<p>I don't understand your diagram.</p>
<p>Forget the gravity, just look at the horizontal force & tension. </p>
<p>Your 'F+ma/2' should be 'F - ma/2', I think. Actually, you just need the tension you show on the LHS of your diagram, which is
Ma + ma/2 = a(M + 0.5m) = (F/ (m+M)) (M + 0.5m) = (F)(M+0.5m)/(m+M)
which simplifies to F(m + 2M) / 2(m + M)</p>
<p>oh yeah, Im so confused with the directions of forces
do u have an MSN or something? i wish to connect u, maybe we can discuss question together while no body can help~~~~</p>
<p>and for this question it has a part asking to prove that the rope is always curve no matter wut.
which because it has a gravity acting down ward, and no other forces acting in y direction.</p>
<p>so i think gravity will have some effect on the rope</p>