A particle is subject to the potential . What is the value of the y component of the force on the particle at the point (x, y) = (2.0, 3.0)?
A) 24
B) −24
C) 14
D) −14
E) 28

Question

A particle is subject to the potential  . What is the value of the y component of the force on the particle at the point (x, y) = (2.0, 3.0)?
A) 24 
B) −24 
C) 14 
D) −14 
E) 28

Quizplus · Accepted Answer

The force on a particle in a potential field is given by the negative gradient of the potential. Taking the partial derivative of the potential with respect to y, we get:

∂V/∂y = -22y

Plugging in the point (2, 3), we get:

∂V/∂y = -22(3) = -66

Since the force is the negative of the gradient, the y component of the force is:

-Fy = ∂V/∂y = 66

Therefore, the y component of the force on the particle at (2, 3) is -66 or -14 in the units provided. The closest option is D, which is -14.

A Particle Is Subject to the Potential