MIT16_07F09_hw04

# MIT16_07F09_hw04 - NAME Massachusetts Institute of...

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Unformatted text preview: NAME : . . . . . . . . . . . . . . . . . . . . . Massachusetts Institute of Technology 16.07 Dynamics Problem Set 4 Out date: Sept 26, 2007 Due date: Oct 3, 2007 Time Spent [minutes] Problem 1 Problem 2 Problem 3 Problem 4 Study Time Turn in each problem on separate sheets so that grading can be done in parallel Problem 1 (10 points) An out of control rocket traces an upward helical trajectory described in cartesian coordinates for t > by x = R cos( ωt ) y = R sin( ωt ) z = v t • A Express the position, velocity and acceleration vectors in the cartesian x, y, z system using unit vectors i, j, k as sketched. • B Express the position, velocity and acceleration vectors in the cylindrical coor- dinate system using unit vectors e r , e θ and k as sketched. • C Express the velocity and acceleration vectors using intrinsic coordinates and the unit vectors unit vectors e t , e n and e b as sketched. • D Where is the center of curvature for this curve when the particle is located at x = 0, y = R ? Problem 2 (10 points) Part A A toy car enters a frictionless elliptical racetrack aligned vertically after being dropped down a frictionless guided slot from a height h under the inﬂuence of gravity. We wish to use intrinsic coordinates to describe its velocity and its acceleration and predict the normal force that it exerts on the track as a function of its position. We describe the ellipse by the parametric equation r ( q ) = aCos ( q ) i + bSin ( q ) j (1) where i and j are the unit vectors in the x and y directions. The parameter q is not the angle θ but is closely related to it. q will give us a unique one-parameter description of this problem.problem....
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MIT16_07F09_hw04 - NAME Massachusetts Institute of...

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