A single conservative force vector F = (4.0x - 12)i hat N where x is in meters, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 20 J at x = 0. (a) Write an expression for U as a function of x, with U in joules and x in meters.
Accepted Solution
A:
Answer:(4.0x - 12)i . (5/3)iStep-by-step explanation:Potential energy = WorkdoneWorkdone = Force x distanceForce = F = (4.0x - 12)i NWorkdone = 20J At x= 0F = -12i /F/= 12Workdone = Force x distance20 = 12 x distanceDistance = 20/12 = 5/3In the vector form distance is written as (5/3)iSince Workdone/ Energy is scalar, U can be expressed as a dot product of the vectors of Force and distance :(4.0 x - 12)i . (5/3)i