Question

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.

Answer 1

Answer:

(4.0x - 12)i . (5/3)i

Step-by-step explanation:

Potential energy = Workdone

Workdone = Force x distance

Force = F = (4.0x - 12)i  N

Workdone = 20J

At  x= 0

F = -12i

/F/= 12

Workdone = Force  x distance

20  =   12 x   distance

Distance =  20/12

               =  5/3

In the vector form  distance is written as (5/3)i

Since 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