Equilibrium: Pendulum from a ceiling to determine accelleration.

AI Thread Summary
A pendulum hanging from an airplane's ceiling is displaced 12 degrees from vertical as the plane accelerates. The tension in the pendulum's cord is analyzed by separating it into vertical and horizontal components. The calculations involve setting the vertical force equal to the weight and the horizontal force equal to the acceleration of the plane. Initially, an incorrect acceleration of 3.57 m/s² was calculated, but after recalculating, the correct answer of 2.1 m/s² was confirmed. The discussion highlights the importance of accurate calculations in physics problems involving forces and angles.
Senjai
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Homework Statement



As an airplane accelerates along a horizontal runway, a pendulum hanging from its ceiling is displaced 12 degrees from the vertical. Calculate the acceleration of the plane.

The Attempt at a Solution


After drawing my diagram, i see that there is a cord supporting the pendulum of weight m. The pendulum is displaced at this instant 12 degrees from the vertical. I know that the tension when separated into components, Tx and Ty, Ty = Fg = mg. And i then assume that Tx is the net horizontal force on the pendulum (i assume it will return to its position of equilibrium as there is no force to hold it in its displacement.)

So i make the calculations:

Ty = mg, Tx = ma
T \cdot cos 12 = mg because the sum of the vertical forces = 0
T \cdot sin 12 = ma because the net force is in the direction of Tx.

I divide the latter by the former to get:

tan 12 = \frac{a}{g} and get 3.57 m/s^2, the answer is 2.1 m/s^2... Not sure how to complete this question.
 
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Senjai, have you got your calculator on radians or something?
g*tan(12) = 2.09 on my calculator.
Nice solution!
 
Uhh.. i don't really know what i did wrong, put it through this time.. got the answer. Thanks, and sorry for wasting your time :( :)
 
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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