Bob's Acceleration and Angle with the Vertical on an Inclined Plane

AI Thread Summary
The discussion revolves around determining the angle a bob makes with the vertical while suspended from a frame sliding down an inclined plane. The acceleration of the frame is identified as g*sin(theta), which is crucial for solving the problem. Participants clarify that the angle phi, which the bob makes with the vertical, equals theta during the slide. The forces acting on the bob include gravitational force and the acceleration due to the frame's motion. Understanding these dynamics is essential for accurately calculating the bob's angle.
Frillth
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Homework Statement



A bob suspended from a frame settles into a steady position relative to the frame as the frame slides down an inclined plane. What angle does the bob make with the during the slide?

Here is the illustration from the book:
http://img237.imageshack.us/img237/9803/plumbbobfs4.jpg

Homework Equations



Unknown. F=ma?

The Attempt at a Solution



I don't really have any idea how to start this problem. I thought the first step would be to calculate that the acceleration of the frame = g*sin(theta), but I don't really know where to go from there. Any ideas?
 
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I left a word out in my original post. It should have said, "What angle does the bob make with the VERTICAL during the slide?"

Also, I found out that the solution is phi = theta, if that would help with working backwards.
 
Frillth said:
I left a word out in my original post. It should have said, "What angle does the bob make with the VERTICAL during the slide?"

Also, I found out that the solution is phi = theta, if that would help with working backwards.

What is the acceleration of the "frame" in which the bob hangs?

As you noted it is M*g*Sinθ for the force so acceleration of the frame must be g*Sinθ .

Now what force is acting on the bob? There is the vertical force m*g acting straight down. What other acceleration is the bob subjected to?
 
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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