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As you can see, $\rho$ only depends on a single variable: $r$. Thus, it should be intuitive that one can do this problem by integrating only over the variable $r$. To see what you are supposed to do, consider what happens if you fix $r$: You obtain a spherical shell (as was pointed out in the comments). The moment of inertia of a spherical shell is quite ...


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See @LDC3's answer for the equations to solve the problem and general explanation. The reason you don't have to worry about gravity in the second equation is because it's assumed the problem gives you the total acceleration of the flea. i.e. gravity has already been considered. In math terms: $ΣF=ma → F_g + F_j = ma$ Because forces are vectors ...


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You need to solve for 2 things. The velocity needed to reach a maximum height of 36mm. The time needed for an acceleration of $3 m/s^2$ to obtain the velocity determine in 1. You use the same equation for both, but change the values for the variables. $$ D=vt+1/2at^2 $$


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Yes, but note that $U_i = K_f$ because $U_f$ is 0 and $K_i$ is 0. The rest of the working seems fine. $ {1 \over 2 }kx^2 = {1 \over 2}mv^2 $ $ {1 \over 2} (1290.9{N \over M})(.275m)^2 = {1 \over 2}(.435kg)v^2$ but we know $N/m = kg/s^2$ $97.62{kg\cdot{m^2} \over s^2} \over (.435kg)$ = $ v^2$ You may have multiplied wrongly. $N/m * m^2 = N\cdot{m}$ and ...


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How do I identify which ones are parallel or series? If all of the current leaving one resistor enters another resistor, the two resistors are in series. The resistances of series connected resistors can be added together to find the equivalent resistance of a single resistor, e.g., $$R_{eq} = R_1 + R_2 $$ If all of the voltage across one resistor is ...


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Since this is a homework type question, I can only offer you a tip and not solve it for you. Tip - Look at this series combination for example Notice that there is some current $I$ flowing through each of these three, and the value of potential at points 1, 2, 3 and 4 (across $R_1$, $R_2$ and $R_3$) aren't the same. On the other hand, in a parallel ...


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You want to work this out in stages. Start at the right hand side where there are three resistors clearly in series. "In series" means that the current that flows through one resistor is equal to the current flowing through the other resistor. The simplest way to identify this is to look for nodes (points where components are connected) with just two wires: ...



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