QuestionDetails: A particle of mass m starts from x 0 m withv 0 >0 m/s. The part

Question

QuestionDetails: A particle of mass m starts from x0 m withv0>0 m/s. The particle experiences the variable forceFx=F0sin(cx) as it moves to the right alongthe x-axis, where F0 and c are constants. a) What are the units of F0? b) What are the units of c? c) At what position xmax does the force first reacha maximum value? Your answer will be in terms of constantsF0 and c and perhaps other numerical constants. d) Sketch the graph of F versus x from x0 toxmax. e) What is the particle's velocity as it reachesxmax? Give your answer in terms of m, v0,F0, and c. QuestionDetails: A particle of mass m starts from x0 m withv0>0 m/s. The particle experiences the variable forceFx=F0sin(cx) as it moves to the right alongthe x-axis, where F0 and c are constants. a) What are the units of F0? b) What are the units of c? c) At what position xmax does the force first reacha maximum value? Your answer will be in terms of constantsF0 and c and perhaps other numerical constants. d) Sketch the graph of F versus x from x0 toxmax. e) What is the particle's velocity as it reachesxmax? Give your answer in terms of m, v0,F0, and c. QuestionDetails: A particle of mass m starts from x0 m withv0>0 m/s. The particle experiences the variable forceFx=F0sin(cx) as it moves to the right alongthe x-axis, where F0 and c are constants. a) What are the units of F0? b) What are the units of c? c) At what position xmax does the force first reacha maximum value? Your answer will be in terms of constantsF0 and c and perhaps other numerical constants. d) Sketch the graph of F versus x from x0 toxmax. e) What is the particle's velocity as it reachesxmax? Give your answer in terms of m, v0,F0, and c.

Explanation / Answer

(a). units of F o is N (b). Units of c is = units of cx / units of x                           = ( rad ) / m                           = rad / m Or units of c is m -1    (c).Given       Fx=F0sin(cx) from problem Fx=F0 from above    sin ( cx ) = 1                             cx = / 2 from this position   x = / 2 c velocity of the particle v = dx / dt we know Fx=F0sin(cx)             (Fx / F0) = sin(cx) from this c x = sin -1 ( Fx/ F0)                 x = ( 1/ c ) sin -1 ( Fx / F0) velocity v = dx / dt                = ( 1/ c ) { 1 / [ 1 - ( Fx / F0) ^ 2] }            from above    sin ( cx ) = 1                             cx = / 2 from this position   x = / 2 c velocity of the particle v = dx / dt we know Fx=F0sin(cx)             (Fx / F0) = sin(cx) from this c x = sin -1 ( Fx/ F0)                 x = ( 1/ c ) sin -1 ( Fx / F0) velocity v = dx / dt                = ( 1/ c ) { 1 / [ 1 - ( Fx / F0) ^ 2] }

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