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ENG102_HW3

ENG102_HW3 - s 1 from the initiation with velocity v How...

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DATE: October 9, 2011 DUE: October 14, 2011 ENG102, homework set #3. 1. Look at Problem 3/101 in the book. a. Solve the problem in the book and give the angle traveled by the mass m . b. The mass has a velocity v 1 [0 ,v 0 ] up until it stops at the distance calculated in 1a. Calculate the distance s 1 and the angle traveled θ 1 as a function of v 1 as well as the other given parameters. c. Draw the normalized distance (2 μ k s 1 /r ) as a function of normalized velocity ( v 1 / rg ) for ( v 0 / rg ) = 1 . We now neglect the gravitational acceleration g . d. Determine the relationship between velocity v 1 and distance traveled s 1 from the initiation with velocity v 0 . How far does the mass travel before it stops? We now change the friction from the kinetic friction proportional to the normal force from the track to a friction that is opposite to the motion and proportional to the velocity; i.e., a frictional force of - α ¯ v . We consider α a known positive constant. e. Determine the relationship between velocity v 1 and distance traveled
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Unformatted text preview: s 1 from the initiation with velocity v . How far does the mass travel before it stops? 2. Look at Problem 3/97 in the book (also look at problem 2/146 that we did in class). a. Write the equation of motion for the particle in polar coordinates r,θ . b. Solve Problem 3/97. We include a friction force f f between the vane and the particle such that ¯ f f =-α ˙ r ¯ e r , where α ≥ is a known constant. c. Write the equation of motion for the particle in polar coordinates r,θ while r ≤ r ≤ R . d. Find the position r ( t ) as a function of the given parameters. e. Find the force ¯ F v exerted exerted by the vane on the particle as a function of time while r ≤ r ≤ R (you can write this as a function of r ( t ) and t ). Niels Grønbech Jensen DEPARTMENT OF MECHANICAL AND AERONAUTICAL ENGINEERING | UNIVERSITY OF CALIFORNIA | DAVIS, CALIFORNIA 95616 TEL: 530.752.5335...
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