In a certain region, the gravitational field is given by E = (5 N/kg ) i + (12 N/kg ) j . Determine the change in potential energy if a particle of mass 2 kg is moved from (12 m , 0) to (0, 5 m ) .

Step-by-step solution

The gravitational field is given by E = 5 i + 12 j N/kg . The gravitational force on the particle of mass m = 2 kg is: F = m E = 2(5 i + 12 j ) = 10 i + 24 j N The initial position vector is r _i = 12 i + 0 j m and the final position vector is r _f = 0 i + 5 j m . The displacement vector of the particle is: r = r _f - r _i = (0 - 12) i + (5 - 0) j = -12 i + 5 j m The work done by the gravitational force is: W = F r = (10 i + 24 j ) (-12 i + 5 j ) W = 10(-12) + 24(5) = -120 + 120 = 0 J The change in potential energy