The gravitational potential in a specific region is given by V = 20 N/kg , (x + y) . Compute the magnitude of the gravitational force acting on a particle of mass 500 g that is located at the origin.

Step-by-step solution

The gravitational field E is given by the negative gradient of the gravitational potential V : E = - ( V x i + V y j + V z k ) Given V = 20(x + y) , the components of the gravitational field are: E_x = - V x = -20 N/kg E_y = - V y = -20 N/kg E_z = - V z = 0 The gravitational field vector is E = -20 i - 20 j N/kg . The magnitude of the gravitational field is: | E | = (-20)^2 + (-20)^2 = 20 2 N/kg The mass of the particle is m = 500 g = 0.5 kg . The magnitude of the gravitational force acting on the particle is: F =