Register to reply

2 masses connected by a string wrapped around a massless pulley, F applied to pulley.

by tonicandgin
Tags: applied, connected, masses, massless, pulley, string, wrapped
Share this thread:
tonicandgin
#1
Feb4-12, 12:28 PM
P: 3
1. The problem statement, all variables and given/known data

m1 and m2 are connected by a massless string wrapped around a massless pulley. An external force F is applied to the pulley. m1 does not equal m2

find the acceleration of each mass, the tension in the string, and the acceleration of the pulley.

F external and m1 and m2 are known.

there is no gravity or friction in the problem.
2. Relevant equations

F=ma



3. The attempt at a solution

What i've worked out so far is that we must consider two reference frames to determine the accelerations. If we can calculate the acceleration of the pulley and the acceleration of one of the masses, the acceleration of the other mass should be determined.

If we consider the pulley's reference frame, one of the masses will be accelerating toward the pulley and the other mass will be accelerating with an equal and opposite acceleration.

If we consider m1, we see the pulley accelerating toward m1 and m2 accelerating with an equal acceleration.

how can we combine these two reference frames to determine the accelerations in the lab frame?

is the acceleration of the center of mass of the system relevant?
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100
tiny-tim
#2
Feb4-12, 12:53 PM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,148
hi tonicandgin! welcome to pf!
Quote Quote by tonicandgin View Post
we must consider two reference frames
no

call the position of the pulley x, call the length of string between the pulley and m1 and m2, respectively, L1 and L2

and use the fact that L1 + L2 must be constant
what do you get?
tonicandgin
#3
Feb4-12, 08:18 PM
P: 3
thanks for the response.

to clarify: what do you mean by "call the position of the pulley x"? is that its position before the force is applied and everything starts moving? or does x change as the system moves?


what i have so far is:

call position of the pulley x. call the length between pulley and the 2 masses L1 and L2, respectively
then position of m1 = x - L1 + 1/2 am1t2
and position of m2 = x - L2 + 1/2 am2t2

i've done a bunch of algebra trying to make use of L1 + L2 = L but nothing seems useful.

I think what i should do is write position equations for each mass and then take two time derivatives to get acceleration, but the only position equations i can write include the accelerations I'm looking for in the first place.

tiny-tim
#4
Feb5-12, 04:40 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,148
2 masses connected by a string wrapped around a massless pulley, F applied to pulley.

hi tonicandgin!

(just got up )
Quote Quote by tonicandgin View Post
does x change as the system moves?
yes, that's the easiest way

then you get

position of m1 = x - L1
position of m2 = x - L2

then call the tension T, and do F = ma for each mass separately
what do you get?
tonicandgin
#5
Feb6-12, 05:48 PM
P: 3
thanks for the help. so far I have:

a1 - ar = ap
a2 + ar = ap

where ar is the relative acceleration of each mass with the pulley.

( m1x1 + m2x2 ) / ( m1 + m2 ) is the center of mass of the system. if we take two time derivatives we get ( m1a1 + m2a2 ) / ( m1 + m2 ) which must equal the only external force, F.

F must = 2T

this is as much as i could get out of my professor today, he seemed to think it was solvable from here, but i still feel like there are too many unknowns and not enough equations.
tiny-tim
#6
Feb7-12, 04:38 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,148
hi tonicandgin!

(just got up )

yes, there are two ways doing it

your can either start with F = ma for the centre of mass, as your professor suggests,

or you can just do F = ma for each of the three bodies separately
Quote Quote by tonicandgin View Post
i still feel like there are too many unknowns and not enough equations.
whichever method you choose, write out all the equations you have, and we'll see


Register to reply

Related Discussions
Acceleration of masses connected with string, non massless pulley Introductory Physics Homework 4
Help with 3 objects/masses connected by string over frictionless pulley? Introductory Physics Homework 5
Two masses on an inclined plane with a massless pulley Introductory Physics Homework 3
3 masses connected by a pulley Introductory Physics Homework 1
2 masses connected by a pulley Introductory Physics Homework 2