Torque Experiment: Finding Mass 2 w/ Given Data

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The discussion centers on conducting a torque experiment to find an unknown mass using a fulcrum setup similar to an unbalanced scale. The participant is unsure how to mathematically approach the problem with the given data, including known mass, radii, and angle of tilt. It is suggested that if the radii are equal, the masses should also be equal for balance; otherwise, the angle of tilt does not contribute to achieving balance. The mathematical relationship involving torque is highlighted, but confusion remains regarding the setup and the role of the angle. Ultimately, the participant seeks clarification on whether their experimental design is correct for determining the unknown mass.
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Homework Statement


So I'm conducting an experiment using simple torque at a set fulcrum, similar to an unbalanced scale (see below), where you know one of the masses and the radii are at equal distances from a central fulcrum and have to find the mass of the other side. I'm having difficulty figuring out how to do this mathematically, if it can be done using just the data given: radii, force of one side, fulcrum. Or perhaps I'm setting it up wrong? Like should there be a counter mass at the top of the fulcrum or something? See: http://is.gd/gasp

Example masses:
r = 6 in
Total length of ruler = 18 inches
Fulcrum at 9 inches
Mass 1: 150g
Mass 2: Unknown
Theta: 25 degrees (let's say like one side is turning downwards at that degree)

400px-Unbalanced_scales_simpler.svg.png


Homework Equations


τ = rFsin(θ)

The Attempt at a Solution


r(m1)(g)sin(θ) = r(m2)(g)sin(90-θ)
 
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Example masses: r = 6 in
What does that mean? I'm not seeing a complete question here.
You say the radii are equal, so the masses must be equal if it is in balance.
If not in balance, the angle of tilt doesn't have any meaning as far as I can see - the thing will just tilt until it runs into some kind of stop because tilting does not cause any balancing - the moments on each side are reduced identically from mgr to mgr*cos A and remain unbalanced.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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