Physics

A uniform chain of total mass m is laid out straight on a frictionless table and held stationary so that one-quarter of its length, L = 1.79 m, is hanging vertically over the edge of the table. The chain is then released. Determine the speed of the chain at the instant when only one-quarter of its length remains on the table.

  1. 👍
  2. 👎
  3. 👁
  1. The easy way to do this is with conservation of energy, since you have to deal with an increasing acceleration rate, which would make the equation of motion rather messy. You can use energy conservation because it is frictionless.

    When it starts out, the center of mass of the chain is (1/2)*(L/4) = L/8 below the table surface.

    When 1/4 of the chain's length remains ion the table, the center of mass is
    (1/2)(3L/4) = 3L/8 below the table surface. The change in CM height is L/4. At that time, the velocity V is given by

    M g L/4 = (1/2) M V^2

    g L = 2 V^2

    V = sqrt(gL/2) = 2.96 m/s

    1. 👍
    2. 👎
  2. LEt total mass be m

    force pulling: masshanging over *g

    force puling: mg*x/1.79 where x is the amount hanging over.

    well, then force pulling is linear with the length hanging over, so the average force between .25x and .75 x is at .5x
    or avg force= mg/2

    Vf^2=Vi^2+2ad
    Vf^2=0+2(avgforce/m)(1/2 1.79)
    Vf= sqrt (g*1.79/2)

    check my thinking.

    Vf= sqrt (2*

    1. 👍
    2. 👎
    👤
    bobpursley
  3. ignore the last line,old typo. I agree with drwls, it is the same argument.

    1. 👍
    2. 👎
    👤
    bobpursley

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    A 4 kg wooden block rest on a table. the coefficient of friction between the block and the table is .40. a 5kg mass is attached to the block by a horizontal string passed over a frictionless pulley of neglible mass what is the

  2. physics

    A 4kg mass moves in a circular path of 7m radius on a frictionless horizontal table. It is attached to a string that passes through a frictionless hole in the center of the table. A second 87kg mass is attached to the other end of

  3. Physics

    A hanging mass, M1 = 0.78 kg, is attached by a light string that runs over a frictionless pulley to a mass M2 = 1.48 kg that is initially at rest on a frictionless table. Find the magnitude of the acceleration, a, of M2 in m/s^2.

  4. ap physics

    Mass m1 on the frictionless table of the figure below is connected by a string through a hole in the table to a hanging mass m2. With what speed must m1 rotate in a circle of radius r if m2 is to remain hanging at rest? (Use any

  1. Physics

    Block A of mass 4.0 kg is on a horizontal, frictionless tabletop and is placed against a spring of negligible mass and spring constant 650 N m. The other end of the spring is attached to a wall. The block is pushed toward the wall

  2. physics

    You create a centripetal force apparatus consisting of a mass m attached to the end of a string and spun in a uniform circular path of radius R, where R = 65.5 cm. The mass is spun in a uniform circular path for 60.0 seconds,

  3. physics

    You know that you can safely stand on the hang-over end of a heavy plank that rests on a table. How far depends on your mass and the mass of the plank. Suppose you can stand on the end of a plank that overhangs the edge of the

  4. physics

    A uniform rod of mass M and length d is initially at rest on a horizontal and frictionless table contained in the xy plane, the plane of the screen. The rod is free to rotate about an axis perpendicular to the plane and passing

  1. physics

    A string is wrapped around a uniform disk of mass M = 1.6 kg and radius R = 0.10 m. (Recall that the moment of inertia of a uniform disk is (1/2)MR2.) Attached to the disk are four low-mass rods of radius b = 0.17 m, each with a

  2. physics

    A puck of mass m = 1.5 kg slides in a circle of radius r = 20 cm on a frictionless table while attached to a hanging cylinder of mass M = 2.5 kg by a cord through a hole in the table. What is the speed of mass m that keeps the

  3. Pls help urgent math

    2/7 part of a cable was laid on the first day, 1/5 part on the second day and 1/3 part was laid on the third day. If 443 1/3m was laid on the fourth day to complete the work, what is the total length of the cable laid?

  4. AP Physics B

    An air puck of mass 0.102 kg is tied to a string and allowed to revolve in a circle of radius 1.06 m on a horizontal, frictionless table. The other end of the string passes through a hole in the center of the table and a mass of

You can view more similar questions or ask a new question.