Respuesta :
Answer:
(a) [tex]\theta=62.31^{\circ}[/tex]
(b) [tex]\theta=117.68^{\circ}[/tex]
Explanation:
It is given that,
Force acting on the particle, F = 12 N
Displacement of the particle, [tex]d=(2.00i -4.00j+3.00k)\ m[/tex]
Magnitude of displacement, [tex]d=\sqrt{2^2+4^2+3^2}= 5.38\ m[/tex]
(a) If the change in the kinetic energy of the particle is +30 J. The work done by the particle is given by :
[tex]W=Fd\ cos\theta[/tex]
[tex]\theta[/tex] is the angle between force and the displacement
According to work energy theorem, the charge in kinetic energy of the particle is equal to the work done.
So,
[tex]cos\theta=\dfrac{W}{Fd}[/tex]
[tex]cos\theta=\dfrac{+30\ J}{12\times 5.38}[/tex]
[tex]\theta=62.31^{\circ}[/tex]
(b) If the change in the kinetic energy of the particle is (-30) J. The work done by the particle is given by :
[tex]cos\theta=\dfrac{W}{Fd}[/tex]
[tex]cos\theta=\dfrac{-30\ J}{12\times 5.38}[/tex]
[tex]\theta=117.68^{\circ}[/tex]
Hence, this is the required solution.
