What is the Period of a Pendulum and String System with a Peg Obstacle?

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The discussion revolves around calculating the period of a pendulum system that includes a peg obstacle. A pendulum with a 10.4m string and a 2.2kg bob is released from a 41-degree angle and swings past a peg 6m below the suspension point. The participants clarify that the period of the pendulum before and after hitting the peg must be considered separately, as it behaves like a simple pendulum in both phases. Key questions focus on the time taken for the bob to drop to the peg, the angle reached after hitting the peg, and the time to swing to that angle. Understanding the conservation of energy is essential for solving the problem effectively.
lonely86driver
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i don't know if I'm making this look easy or hard but here's the question

A pendulum made of a string of length 10.4m and a spherical bob of mass 2.2kg is able to swing in a vertical plane. The pendulum is released from an angular position 41* from vertical. The string hits a peg located a distance 6m below the point of suspension and swings about the peg up to an angle "a" on the other side of the peg. the bob proceeds to oscillate back and forth between these two angular extremities. acc. of gravity is 9.8 m/s^2. what is the period of the pendulum plus the peg system shown above.

since period only depends on length of the string and acceleration due to gravity
this is what i was thinking about the problem. i just add two periods togethers. but then reading the problem again its sounds like i need to find the period of the second system in order to find the complete period of the entire system.

it sounds like the second system is a torsional pendulum problem so i might have to find the period for that.
i wish i had a pic to post up but i don't have it on my computer.
 
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lonely86driver said:
it sounds like the second system is a torsional pendulum problem so i might have to find the period for that.

It's nothing like that. You have a simple pendulum before and after the string touches the peg.

Try to answer the following questions, in order.

1.) How long does it take for the bob to drop from its release point to the peg?

2.) What must the angle a be after the string hits the peg? (Hint: What quantity must be conserved here?)

3.) How long does it take for the bob to get to the angle a after the string hits the peg?
 
ahhh i see now thanks
 
Let us know if you get stuck.
 
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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