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Unable to render embedded object: File (Boxcar and Cannonballs 01.xls) not found.

Imagine that you have an indestructible boxcar sitting on frictionless railroad track. The boxcar has length L, height H, and width W. It has N cannonballs of radius R and mass M stacked up against one end. If I move the cannonballs in any fashion – slowly carrying them, rolling them, firing them out of a cannon – what is the furthest I can move the boxcar along the rails? Which method should I use to move the boxcar the furthest? Assume that the inside walls are perfectly absorbing, so that collisions are perfectly inelastic.

Part A

Solution One

System:

Interactions:

Model:

Approach:

Diagrammatic Representation

Unable to render embedded object: File (thatfbd1.jpg) not found.

the system consists of the Boxcar on rails and the Cannonballs, plus whatever devices we use for propulsion inside.There are thus no external influences

Mathematical Representation

Since there are no external influences, which includes forces, the center of mass of the system is not affected, and by the Law of Conservation of momentum must remain fixed. .

Unknown macro: {latex}

\begin

Unknown macro: {large}

[\ M_

Unknown macro: {Boxcar}

x_

Unknown macro: {Boxcar, initial}

+ \sum M_

Unknown macro: {i}

x_

Unknown macro: {i, initial}

= M_

x_

Unknown macro: {Boxcar, final}

+ \sum M_

Unknown macro: {i}

x_

Unknown macro: {i, final}

]\end

Here xi is the position of the center of the *i*th cannonball and xBoxcar is the position of the center of the boxcar. The subscripts initial and final indicate the positions at the start and the end of our operation.

Unknown macro: {latex}

\begin

Unknown macro: {large}

[ N = F_

Unknown macro: {A}

= \mbox

Unknown macro: {300 N}

]\end

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