phys124s11-l04

# phys124s11-l04 - Physi cs 124 Spr i ng 2010 Lecture 3...

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1 Physi cs 124, Spr i ng 2010 Lecture 4 Outline + Summary Lecture 3 review : fluids Pressure, Pascal, Archimedes, Bernoulli, Toricelli, etc. Newton's Law: F 1 on 2 =− G m 1 m 2 | r 12 | 2 r 12 = m 1 g r 12 points from 1 to 2 Kepler's 1 st law : elliptical orbits with the sun at one focus. Kepler's 2 nd law : orbit sweeps out equal areas in equal times Kepler's 3 rd law : T 2 a 3 = constant = 4 2 Gm sun Gravitational field g = F g m =− GM r 2 r Conservative force: U =− GMm r = GMm r 2 dr mgh near earth Recall: only U matters

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2 Physi cs 124, Spr i ng 2010 Let's start with a clicker question Two objects of equal size are dropped. a: A falls twice as fast as B. e: The one with the larger gravitational mass falls faster. d: A and B weigh the same, so they fall at the same rate. c: A weighs twice as much as B, but they fall at the same rate anyway. demo The mass of A is twice the mass ofB. Which of the following is true ? Neglect air resistance. b: B falls twice as fast as A.
3 Physi cs 124, Spr i ng 2010 Two objects of equal size are dropped. a: A falls twice as fast as B. The mass of A is twice the mass ofB. Historically, it was thought that heavier masses fell faster, and this does seem to make intuitive sense. Galileo proved it wrong. (early 1600s) The idea neglects Newton's Law: F = ma, where F = W = mg, the weight, and thus both sides of the equation are proportional to the mass. (late 1600s) But why the inertial mass and the gravitational mass are the same thing can be viewed as one of those difficult philosophical questions

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4 Physi cs 124, Spr i ng 2010 Near-earth gravity The force of gravity is: F g = m g demo g = 9.8 m / s 2 , the acceleration of gravity at earth's surface Newton's 2 nd law: F = m a The gravitational mass in F g = mg is the same as the inertial mass in F = m a. An approximation valid near the surface of the earth. Thus m g = m a and a = g Neglecting air resistance, all objects accelerate the same.
Physi cs 124, Spr i ng 2010 Another clicker question Astronaut Jane observes balls of mass 1 and 2 kg a: F 1 on 2 = 2F 2 on 1 . c: 1 and 2 have the same acceleration. d: There is no gravity in space, so they do not accelerate. e: All other answers are wrong. demo floating free in space. Which of the following is true ?

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phys124s11-l04 - Physi cs 124 Spr i ng 2010 Lecture 3...

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