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Unformatted text preview: Math 317, Section 202, Homework no. 6 (due Wednesday (!) March 3, 2010) [10 problems, 48 points + 8 bonus points] Problem 1 (6 points) . An object of mass m = 2 moves along the trajectory (1) r ( t ) = t 4 2 i- t 4 j + t 4 4 k , t 1 , (2) r ( t ) = 1 2 cos t i- 1 2 cos t j + sin t k , t 2 . Time is denoted by t . For each trajectory (1) and (2), (a) determine the tangential and the normal component of acceleration, (b) find the force F ( t ) that acts on the object, as a function of time, (c) compute the work done by F in moving the object along the trajectory. (1 point for each combination of part (a) to (c) with a trajectory (1) or (2)) Problem 2 (8 points) . Consider the force given by the vector field F ( x,y,z ) = c h z,x,zy i , with some constant c . (a) (6 points, 2 points for each trajectory) Compute the work done by the force F in moving a particle of mass m = 1 along each of the following trajectories. t denotes time. (1) r ( t ) = h t, , 3- 3 t i , 1 t 2, (2) r ( t ) = h 2 t, , 3- 6 t i , 1 / 2 t 1, (3) r ( t ) = t, ,...
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