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Classical Mechanics Problems

Classical Mechanics Problems - Classical Mechanics(Escape...

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Classical Mechanics (Escape Velocity) Problem 1 Suppose the Moon were to have the same mass as the Earth, and you are trying to throw one of your physics books from the Earth to the Moon. With what minimum velocity must the book leave the surface of the Earth? Neglect the relative motion of the Earth and them Moon, and the Earth’s rotation. The mass of the Earth is ME = 6.0·1024 kg, the radius of the Earth is 6.4 · 106 m, and the distance from the center of the Earth to the center of the Moon is REM = 3.8 · 108 m. Compare your answer to the escape velocity from Earth alone. The gravitational constant is G = 6.67 · 10 11 N m2/kg2. Classical Mechanics Problem 2 A wedge of mass M=4.5 kg sits on a horizontal surface. Another mass m=2.3 kg sits on the sloping side of the wedge. The incline is at an angle θ =31.7 degrees with respect to the horizontal, and g=9.8 m/ . All surfaces are frictionless. The mass m is released from rest on mass M, which is also initially at rest. Use Lagrangian mechanics and the
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