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1.A particle moves in the xy plane under the constraint that its velocity vector is always directed toward a point on the x axis whose abscissa is some given function of time f(t). Show that for f(t) differentiable, but otherwise arbitrary, the constraint is nonholonomic.
2.A particle of mass m is constrained to move on the surface of a sphere of radius R by ab applied force F (θ, A~). Write the equation of motion.
3.The area of the Earth’s surface is approximately 516 X 106 km2. What is the weight of the entire atmosphere in tonnes? Express your answer using scientific notation, in units of 1012 tonnes.
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4.A hydrogen atom has a diameter of approximately 1.06 x 10-10 m, as defined by the diameter of the spherical electron cloud around the nucleus. The hydrogen nucleus has a diameter of approximately 2.40 X 10-15 m.
(a) For a scale model, represent the diameter of the hydrogen atom by the length of an American football field (100 yd $ 300 ft), and determine the diameter of the nucleus in millimeters.
(b) The atom is how many times larger in volume than its nucleus?
5.A hydrogen atom is in its eighth excited state, corresponding to n = 9.
(a) Find the radius of the electron’s Bohr orbit.
(b) Find the de Broglie wavelength of the electron in this orbit.
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