# Object and bead on a pulley

#### Isiltir

Need help with this excercise.

There is a pulley. On the left side hangs object of Mass M and height L. On the other side a bead of mass m slides down the rope. After release from rest, bead passes the Object in time T.

What is the friction force (lets call it "P") of the bead?
What is the acceleration of bead ("a") and the object ("A") in reference to Earth?

So Newtons 2nd law for object M: MA= Mg - P
for bead m: ma= mg - P

So P= mg - ma and I am supposed to find a using L and T?

#### Woody

Am I correct in my understanding?
After release both the bead and the mass M are falling?
The rate of fall of the bead will be reduced by the friction of the bead on the rope.
However, the friction of the bead on the rope will also apply a force to the rope,
which will slow the rate at which the mass M falls (because it is connected via the pulley).

#### Isiltir

Yes. So I figured out that in object's reference frame, the bead is moving with relative acceleration "arel" that we can calculate (arel=2L/T²). Futhermore, arel= a - A so A= a - arel.

Now I can calculate both accelerations using
mg - ma = Mg - M (a - 2L/T²) as well as P. Is that right?