Lecture11-2A_000

Lecture11-2A_000 - Today's Lecture Lecture 11: Chapter 6,...

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Today Today s Lecture s Lecture Lecture 11: Chapter 6, Using Newton’s Laws Rotational Examples Drag
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First Example: Two Football Players and First Example: Two Football Players and the Female Gymnast the Female Gymnast There is a standard demonstration in a mechanics class where two large football players pull on a rope putting as much tension as possible in the rope. Then the smallest girl in the class is asked to pull (in the transverse direction) on the middle of the rope with her smallest pinky finger. Let’s examine what happens. The free-body diagram is: The EOM’s for both the x and y direction: Since she pulls in the middle of the rope q 1 = q 2 From the x equation this implies that T 1 = T 2 = T . T 1 x T 2 x T 1 cos 1 T 2 cos 2 0 T 1 y T 2 y f T 1 sin 1 T 2 sin 2 f 0
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First Example: Two Football Players and First Example: Two Football Players and the Female Gymnast the Female Gymnast The equation for the y components simplifies to: For q small, sin q = tan q, and the transverse displacement of the rope, d y, is: We see that when L , the length of the rope, is large, the girl with her pinky will be able to deflect the rope in the transverse direction even when f/T<<1 . Two large football players pull on a rope putting as much tension as possible in the rope. Then the smallest girl in the class is asked to pull (in the transverse direction) on the middle of the rope with her smallest pinky finger. Let’s examine what happens. The free-body diagram is: T 1 sin 1 T 2 sin 2 f 0 2 T sin f y f 4 T L
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Assuming frictionless surfaces, find the acceleration of m 2 . From a free-body diagram the vector EOM for m 1 is: Choosing a coordinate system in which the x axis is parallel to the incline the component equations are: The EOM for m 2 is particularly simple: It is important to note that we have assumed that m 2 is accelerating down and m 1 is accelerating up the incline. We could have done the reverse, but we must be consistent. That is, m 1 and m 2 cannot both accelerate up (or down). T N F g m a T m 1 g sin m 1 a and N m 1 g cos 0 m 2 g T m 2 a
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Assuming frictionless surfaces, find the acceleration of m 2 . The two relevant equations are:
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Lecture11-2A_000 - Today's Lecture Lecture 11: Chapter 6,...

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