15 lines
770 B
Markdown
15 lines
770 B
Markdown
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section: Conservation laws
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PROBLEM
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A particle of mass m moving with velocity V1 leaves a half-space in which its potential energy
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is a constant U1 and enters another in which its potential energy is a different constant U2.
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Determine the change in the direction of motion of the particle.
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SOLUTION. The potential energy is independent of the co-ordinates whose axes are parallel
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to the plane separating the half-spaces. The component of momentum in that plane is
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therefore conserved. Denoting by 01 and O2 the angles between the normal to the plane and
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the velocities V1 and V2 of the particle before and after passing the plane, we have V1 sin 01
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= U2 sin O2. The relation between V1 and V2 is given by the law of conservation of energy,
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and the result is
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sin
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