A glider is on a friction-less track connected to a hanging weight by a thread going over a pulley. Does the mass of the thread affect the acceleration measurement? if so, explain.
A glider is on a friction-less track connected to a hanging weight by a thread going over a pulley. Does the mass of the thread affect the acceleration measurement? if so, explain.
bump
Not 100% certain, but I think it would because the thread is adding to the mass which is being accelerated. As the glider moves, more thread will be over the pulley so the thread will be more of a contribution to the pulling force of the hanging weight. These type of problems usually assume a negligible mass for the thread, but you could account for it by expressing the additional mass as a function of the length.
not newton wrote:
A glider is on a friction-less track connected to a hanging weight by a thread going over a pulley. Does the mass of the thread affect the acceleration measurement? if so, explain.
Do your own homework.
not newton wrote:
A glider is on a friction-less track connected to a hanging weight by a thread going over a pulley. Does the mass of the thread affect the acceleration measurement? if so, explain.
If this is an introductory physics course, you can safely assume that the pulley is massless. Usually they'll say so explicitly, as with kinetics problems involving projectile motion ("neglect air resistance"), but not always.
CB22 wrote:
Not 100% certain, but I think it would because the thread is adding to the mass which is being accelerated. As the glider moves, more thread will be over the pulley so the thread will be more of a contribution to the pulling force of the hanging weight. These type of problems usually assume a negligible mass for the thread, but you could account for it by expressing the additional mass as a function of the length.
CB22 is right.
i support this. the mass is growing at an accelerated rate.
horizontal component of the string, mass has no effect.
vertical component of string, mass has effect.
not trying to separate the string into vector components.
Just to clarify bangalangadanga's comment, the mass of the entire string contributes to the total mass (string plus glider plus hanging weight) which is being accelerated by the hanging part.
However, only the mass of the vertical part of the string (which becomes more of the string as the glider slides) contributes to the gravitational force that is pulling on the glider (mass of hanger plus mass of string that is currently vertical, times g).
As for the comment about the pulley, you can ignore it. But if the pulley had a nonzero mass and a nonzero radius, then it would take energy to make the pulley start moving, and you would have to take that into account too. The glider would accelerate more slowly in this case, because some of the potential energy of the falling hanger would go toward making the pulley turn.
The length, not the mass, of the thread affects the acceleration measurement.
hahahahahah wrote:
The length, not the mass, of the thread affects the acceleration measurement.
This is wrong. What matters it the total mass of the string, and the mass of the part of the string that is hanging down from the pulley.
You'll probably want to express the mass of string which is hanging from the pulley at each moment as a function of the length of hanging string. To do this you'll want to know the linear density of the string (how much it weighs per unit length at each point). If the string has the same linear density everywhere, then this is just M/L, where M is the mass of the whole string and L is its length. So when a third of the string is hanging over, the mass of that part is M/3. Etc.
So, the second paragraph is a way that the length of the string could possibly come into play indirectly, as a way to help you figure out one of the two numbers that matters. (That is, it could help you figure out the mass of the part of the string that is hanging down.)
Force = ma
Force = (m1+m2)(9.8 m/s^2)
Force = (weight+string)(9.8m/s^2)
Force is increasing since mass of (weight + string) is increasing.
Mass of (horizontal string + trolley) is decreasing.
I'm a bit rusty, but I'm quite certain that placing a cubic inch of lead versus a cubic inch of water will yield different results.
Ok I said do your own homework but these guys are being seriously confusing.
The mass of the string matters here for two reasons:
1. Accelerations: F = ma, so larger masses accelerate more slowly.
2. Gravity: F = mg, so more hanging mass means there's a larger gravitational force.
The mass contributing to gravity and the mass being accelerated are not necessarily the same.
Might as well be a little clearer...
Let 'Mh' be the mass of the hanging weight, 'Mb' be the mass of the gliding block, and 'Ms' be the mass of the string, whose length is 'L'.
Then the force provided by gravity when a length 'x' of string is hanging is:
Fg = (Mh + Ms*x/L)*g
This force provides an acceleration to the whole system:
Fg = (Mh + Mb + Ms)*a
So
a = (Mh + Ms*x/L)*g / (Mh + Mb + Ms)
a = dx/dt, so this gives you a first order differential equation to solve.
Let A = Mh / (Mh + Mb + Ms), and let B = g*Ms / L*(Mh + Mb + Ms).
Then dx/dt = A + B*x.
Note that x(t) = C*exp(B*t) - A/B is a solution for any C with dC/dt = 0. (I found this using undetermined coefficients.)
Impose x(0) = x0 as an initial condition to pick the correct C, and we get C - A/B = x0, which implies C = x0 + A/B.
So now we have an equation for the amount of string hanging over the pulley, x(t), at time t, assuming that at t=0 we started with a length of string x0 hanging over the pulley.
x(t) = (x0 + A/B)*exp(B*t).
42
A simple way to answer this -- does the question even include the mass of the string? And what level physics course is this? It it calculus-based or algebra-based?
I majored in physics back when "string theory" had more to do with scanty underwear than the fundamental components of matter, and only when I got to advanced-level mechanics did I see problems introducing this kind of wrinkle.
wepmad wrote:
Ok I said do your own homework but these guys are being seriously confusing.
The mass of the string matters here for two reasons:
1. Accelerations: F = ma, so larger masses accelerate more slowly.
2. Gravity: F = mg, so more hanging mass means there's a larger gravitational force.
The mass contributing to gravity and the mass being accelerated are not necessarily the same.
In any case, I have now written out an explicit solution to the problem, which should make things as clear as possible. But I already thought I had articulated wepmad's two points fairly clearly:
"the mass of the entire string contributes to the total mass (string plus glider plus hanging weight) which is being accelerated by the hanging part.
However, only the mass of the vertical part of the string (which becomes more of the string as the glider slides) contributes to the gravitational force that is pulling on the glider (mass of hanger plus mass of string that is currently vertical, times g)."
right, for all practical purposes and applicatins, you can get away with fudging the numbers a bit... at least in newtonian mechanics
the purpose of vague is to better emphasize general concepts which at the end of the day was the best way i learned physics.
You won't get into variable mass acceleration problems until you derive the rocket science rules. Assume mass-less pulley and mass-less string.
you need letsrun to help you with this?
Yeah dude, assume the pulley and string are massless. The only part that is going to affect the acceleration is the gravitational pull from the mass. If you're working with a frictionless surface, you can for sure assume the string is going to be negligible.