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

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

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