I've got to find things out about these pendulums

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The discussion focuses on a pendulum problem where a bob starts swinging from a height of 0.3000 m, losing 1.00% of its energy due to friction with each swing. Participants are encouraged to determine the potential energy (PE) at various heights after each swing to find the maximum height after the fourth swing. The initial potential energy is calculated based on the starting height, and subsequent heights must account for the energy lost in each swing. The conversation emphasizes the importance of breaking down the problem step by step to arrive at a solution. Understanding the relationship between potential energy and height is crucial for solving this type of physics problem.
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Homework Statement



The pendulum is started swinging from a height of 0.3000 m above its rest position and allowed to swing freely back and forth. If 1.00% of the bob's energy is lost due to friction each swing, to what maximum height will the bob swing at the end of its fourth swing?

Homework Equations



I cannot even begin to think of any

The Attempt at a Solution



h=0.3000m
energy lost=1.00%/swing
max h=?

PEi + KEi = PEf + KEf + HE
 
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thear said:

Homework Statement



The pendulum is started swinging from a height of 0.3000 m above its rest position and allowed to swing freely back and forth. If 1.00% of the bob's energy is lost due to friction each swing, to what maximum height will the bob swing at the end of its fourth swing?

Homework Equations



I cannot even begin to think of any

The Attempt at a Solution



h=0.3000m
energy lost=1.00%/swing
max h=?

PEi + KEi = PEf + KEf + HE

Welcome to the PF.

What is the equation for the PE of the pendulum as a function of height? What is the initial PE? What is the PE after the 1st swing? After the 2nd, after the 3rd, after the 4th? And so what is the height after the 4th swing?

Try talking problems like this through, and you will be able to at least show an attempt at a solution when you post the problems here...
 
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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