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.

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Mathematics

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7 December, 05:17

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.

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Valerie Soto · Answer 1

(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