How Do Pulses Travel in Strings of Different Densities?

AI Thread Summary
The discussion focuses on a physics problem involving two strings with different linear densities—2.4 g/m for string 1 and 3.5 g/m for string 2—tied together at the middle. The objective is to determine the lengths of each string, given that the combined length is 4 meters and the pulses must reach the ends simultaneously. To solve the problem, one must apply the relationship between wave speed, tension, and linear density in the strings. The key is to find the lengths that allow for equal travel times for the pulses. Understanding these principles is essential for solving the homework question effectively.
paulsberardi
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Homework Statement


String 1 in the figure has linear density 2.4 g/m and string 2 has linear density 3.5 g/m. A student sends pulses in both directions by quickly pulling up on the knot, then releasing it. Consider the pulses are to reach the ends of the strings simultaneously.
In the figure: The two strings are tied together in the middle and the combined strings have a length of 4m.

Homework Equations


What is the length of string one and what is the length of string 2?
 
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please show your attempt to solve the question ..
 
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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