2005exam1 - M travelling through a Fuid is proportional to...

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PHYSICS 321 EXAM 1 Feb 16, 2005 NAME 1. [3 pts] The location of a particle of mass M is given by ~ r = C 1 cos( ω t ) ˆ i + C 2 e B t ˆ j + C 3 t 3 ˆ k as a function of the time t , where C 1 , C 2 , C 3 , B , and ω are constants. Find the component of force in the tangential direction.
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2. A mass M is attached to the ceiling by a massless string of length b . The mass is swinging back and forth, so θ is a function of time. Your answer to each question should contain some or all of the following: θ , ˙ θ , ¨ θ . (a) [2 pts] Write down the kinetic energy. (b) [2 pts] Write down the angular momentum about the point where the string is at- tached to the ceiling. (c) [3 pts] Use the radial component of ~ F = M ~a to Fnd the tension in the string. (d) [3 pts] Use the tangential component of ~ F = M ~a to Fnd the equation of motion which relates ¨ θ to θ .
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3. [5 pts] Suppose that the friction force on an object of mass
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Unformatted text preview: M travelling through a Fuid is proportional to the cube of the velocity: F =-K v 3 , where K is a constant. ind the velocity as a function of time, assuming that the initial velocity is v at time t =0. Neglect gravity. 4. A chain with length b and uniform mass density is tightly coiled up on the Foor. One end of the chain is lifted straight up at a rate such that the height of that end above the Foor is given by x = K t 3 , where K is a constant. (a) [4 pts] ind the total force on the chain as a funtion of time t . (b) [4 pts] ind the height of the center of mass of the entire chain as a function of time t . (c) [4 pts] ind the work done by the hand as a function of time t ....
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2005exam1 - M travelling through a Fuid is proportional to...

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