Recent content by supermanii

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    Ideal Gas Carnot engine refrigeration

    Homework Statement What is the relationship between the heat absorbed and rejected by the reservoirs and their temperature. If a heat pump is used to transfer heat what is the rate at which heat is added to the hot reservoir in terms of the temperatures of the reservoir and the work done by...
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    Proof of Conservation of Vector Calculus: Force on a Mass with Position Vector r

    Ok I was wrong, but dr/dt cross itself goes to zero so: \frac{dL}{dt}=\frac{d^{2}r}{dt^{2}}\times r? I have to prove that \frac{d^{2}r}{dt^{2}} and r are in the same direction. Am I right in thinking that the very first equation shows exactly this? As both m and f(r) are scalars so do not...
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    Proof of Conservation of Vector Calculus: Force on a Mass with Position Vector r

    Yes I know the product rules for cross products. So: \frac{dL}{dt}=\frac{dr}{dt}\times\frac{dr}{dt}+\frac{d^{2}r}{dt^{2}}\times r All the derivatives of and r itself are in the same direction so all go to 0 thus proving L is conserved :). Thanks for the help.
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    Proof of Conservation of Vector Calculus: Force on a Mass with Position Vector r

    A 2nd year undergraduate physics module called mathematical methods.
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    Proof of Conservation of Vector Calculus: Force on a Mass with Position Vector r

    Homework Statement The Force on a mass with position vector r satisfies: m\frac{d^{2}\textbf{r}}{dt^{2}}=F=f(\textbf{r})\textbf{r} where f(r) is scalar function of r. Show that L: L=\textbf{r}\times\frac{d\textbf{r}}{dt} is conserved. Homework Equations The Attempt at a...
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