Question

A 12 N force with a fixed orientation does work on a particle as the particle moves through displacement What is the angle between the force and the displacement if the change in the particle's kinetic energy is (a) +8.49 J and (b) -8.49 J?

Answer 1

given

F = 12 N

d = 4 i - 5 j + 3 k

+ 8.49J , - 8.49 J

a )

cos $\small \theta$ = (+8.49) / 12 ( 4² + (-5)² + 3² )

cos $\small \theta$ = 8.49 / 12 ( 50 )

cos $\small \theta$ = 8.49 / 600

cos $\small \theta$ = 0.01415

$\small \theta$ = cos^-1(0.01415)

$\small \theta$= 89.189⁰

b )

cos $\small \theta$ = (-8.49) / 12 ( 4² + (-5)² + 3² )

cos $\small \theta$ = -8.49 / 12 ( 50 )

cos $\small \theta$ = - 8.49 / 600

cos $\small \theta$ = - 0.01415

$\small \theta$ = cos^-1(-0.01415)

$\small \theta$= 90.81⁰