A 13 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) +9.19 J and (b) -9.19 J?
To find the angle between the force and the displacement, we can use the work-energy principle. According to the principle, the work done on an object is equal to the change in its kinetic energy. The work done is given by the equation:
Work = Force * Displacement * cos(theta)
where theta is the angle between the force and displacement vectors.
Let's calculate the angle for each case:
(a) When the change in kinetic energy is +9.19 J:
We have Work = +9.19 J, and let's assume the displacement is positive. The equation becomes:
9.19 J = 13 N * Displacement * cos(theta)
From this equation, we can solve for the angle theta:
cos(theta) = 9.19 J / (13 N * Displacement)
To find the angle, we need to know the value of Displacement. If you have that information, substitute it into the equation and solve for cos(theta). Finally, take the inverse cosine (cos^-1) of the resulting value to get the angle theta.
(b) When the change in kinetic energy is -9.19 J:
Similarly, we have Work = -9.19 J, and let's assume the displacement is positive:
-9.19 J = 13 N * Displacement * cos(theta)
Following the same steps as in case (a), substitute the value of Displacement and solve for cos(theta). Take the inverse cosine (cos^-1) of the resulting value to get the angle theta.