Displacement of centre of mass


by utkarshakash
Tags: centre, displacement, mass
utkarshakash
utkarshakash is offline
#1
Sep13-12, 02:15 AM
P: 638
1. The problem statement, all variables and given/known data
A pulley fixed to a rigid support carries a rope whose one end is tied to a ladder with a man and the other end to a counterweight of mass M. The man of mass m climbs up a distance h with respect to the ladder and then stops. If the mass of the rope and the friction in the pulley axle are negligible, find the displacement of the centre of mass of this system.


2. Relevant equations
COM[itex]_{y}[/itex]=my[itex]_{1}[/itex]+my[itex]_{2}[/itex]/m+M


3. The attempt at a solution
Let the y-coordinate of man be l and that of mass M be 0. Since it goes up a height h
∴ y-coordinate of the man changes to (l+h) but that of mass M remains unchanged.
So, if I subtract the final COM from initial COM I get the answer mh/m+M. But the correct answer is mh/2M. I'm unable to bring out mistake in my solution.
Phys.Org News Partner Science news on Phys.org
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)
rl.bhat
rl.bhat is offline
#2
Sep13-12, 02:57 AM
HW Helper
P: 4,442
Before man starts climbing the ladder, whether the system is in equilibrium? If yes, you have to take into account the mass of the ladder, which is M- m.
utkarshakash
utkarshakash is offline
#3
Sep13-12, 08:04 AM
P: 638
Oh, I forgot that the system is in equilibrium. I must have noticed the word counterweight. This is the key to the answer. Thanks so much as now I have arrived at the correct answer.


Register to reply

Related Discussions
Mass-spring-mass system rotating about its centre of mass relativistically Advanced Physics Homework 0
centroid,centre of mass and centre of gravity Introductory Physics Homework 5
Question about centre of mass and load centre of gravity General Engineering 3
centre of mass vs. centre of gravity Classical Physics 1
HELP : Centre of mass and Centre of gravity Introductory Physics Homework 5