• Support PF! Buy your school textbooks, materials and every day products Here!

Falling Rope on a scale

  • Thread starter SonOfOle
  • Start date
  • #1
42
0

Homework Statement


A uniform flexible rope is suspended above a scale, with the bottom of the rope just touching the scale (gravity points downward). The rope has a length L and a total mass of M. The mass is uniformly distributed along it's length.

The rope is released. After a length x<L has fallen onto the scale, what does the scale read? Assume the scale can measure the force applied to it instantaneously. (Hint: the force exerted by the rope on the scale has two components).

Homework Equations





The Attempt at a Solution


F=dp/dt
p=m*t
m(t)=(M/L)*v(t)
so p(t)=(M/L)*(v(t)^2)
=(M/L)*(g^2)*(t^4)/4
thus dp/dt=(M/L)*(g^2)*t^3

also, x(t)=g(t^2)/2--> t=sqrt(2xg). plug that into the eqn for dp/dt, and get
F(x)=dp/dt=(M/L)*(g^2)*(2xg)^(3/2).

However, that solution doesn't treat the problem with a force of two components, nor do the units seem to work out. Any ideas?
 

Answers and Replies

  • #2
238
0
Let M=mass, L=length of the rope, v=velocity

You have to express in component form,
[tex]F_{net} + \frac{dm}{dt}v=m\frac{dv}{dt} [/tex]
[tex]= F_{n} - mg+\frac{dm}{dt}v=0[/tex] (Eq 1), then

[tex]\frac{dm}{dt}=\frac{-M}{L}v[/tex] (*), where dm=mass of the section of the rope that falls on the scale.

Substitute (*) back into (Eq 1) and find v using [tex]v^2=v_{0}^2+2a\Delta y[/tex]
Then find [tex]F_n[/tex]
 
  • #3
42
0
thanks
 

Related Threads for: Falling Rope on a scale

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
4
Views
805
  • Last Post
Replies
19
Views
1K
Replies
7
Views
698
  • Last Post
2
Replies
46
Views
2K
Replies
4
Views
2K
Top