- #1
inkliing
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This isn't homework...I'm reviewing physics after many years of neglect.
Given 2 masses, [itex]m_1, m_2[/itex], connected by a rigid, massless rod, stationary with respect to a ramp which makes an angle of [itex]\theta[/itex] with the horizontal, with coefficients of static friction between the masses and the ramp = [itex]\mu_{s1}, \mu_{s2}[/itex] respectively, what is the magnitude of the tension or compression in the rod, and what are the magnitudes of the static friction, [itex]f_{s1}, f_{s2}[/itex], acting on each mass?
This assumes [itex]\theta[/itex] is small enough that the masses do not lose traction, i.e.,
[tex]\theta \leq \arctan \frac{\mu_{s1} m_1 + \mu_{s2} m_2}{m_1 + m_2}[/tex]
Note that if the masses are assumed to already be moving, then the problem is straightforward:
[tex]T = (\mu_{k1} - \mu_{k2})\frac{m_1 m_2}{m_1 + m_2}g\cos\theta[/tex]
[tex]f_{k1} = \mu_{k1} m_1 g\cos\theta[/tex]
[tex]f_{k2} = \mu_{k2} m_2 g\cos\theta[/tex]
Where T is the tension in the rod (T<0 implies compression). Such problems are common in basic physics, e.g., Halliday, Resnick, & Krane, 4th Ed., chap.6, problem 29.
So I assumed it would be straightforward to do the same problem, but with the masses stationary. But I get 2 equations (sum of the forces for each mass) and 3 unknowns (T, [itex]f_{s1}, f_{s2}[/itex]).
I find it surprising that such a simple situation is undetermined, and assume I've missed something simple.
Note: I've looked through several physics texts and can find only problems in which the masses are already moving.
Also, it's driving me crazy!
Given 2 masses, [itex]m_1, m_2[/itex], connected by a rigid, massless rod, stationary with respect to a ramp which makes an angle of [itex]\theta[/itex] with the horizontal, with coefficients of static friction between the masses and the ramp = [itex]\mu_{s1}, \mu_{s2}[/itex] respectively, what is the magnitude of the tension or compression in the rod, and what are the magnitudes of the static friction, [itex]f_{s1}, f_{s2}[/itex], acting on each mass?
This assumes [itex]\theta[/itex] is small enough that the masses do not lose traction, i.e.,
[tex]\theta \leq \arctan \frac{\mu_{s1} m_1 + \mu_{s2} m_2}{m_1 + m_2}[/tex]
Note that if the masses are assumed to already be moving, then the problem is straightforward:
[tex]T = (\mu_{k1} - \mu_{k2})\frac{m_1 m_2}{m_1 + m_2}g\cos\theta[/tex]
[tex]f_{k1} = \mu_{k1} m_1 g\cos\theta[/tex]
[tex]f_{k2} = \mu_{k2} m_2 g\cos\theta[/tex]
Where T is the tension in the rod (T<0 implies compression). Such problems are common in basic physics, e.g., Halliday, Resnick, & Krane, 4th Ed., chap.6, problem 29.
So I assumed it would be straightforward to do the same problem, but with the masses stationary. But I get 2 equations (sum of the forces for each mass) and 3 unknowns (T, [itex]f_{s1}, f_{s2}[/itex]).
I find it surprising that such a simple situation is undetermined, and assume I've missed something simple.
Note: I've looked through several physics texts and can find only problems in which the masses are already moving.
Also, it's driving me crazy!