(c) A force field is given by the potential U=x^2+2y^2+z^3+2xy+2yz+z Find the work done by the force field in inoving a particle from the point (1,1,2) to (2,1,2) (3 marks)

Question

(c) A force field is given by the potential U=x^2+2y^2+z^3+2xy+2yz+z Find the work done by the force field in inoving a particle from the point (1,1,2) to (2,1,2) (3 marks)

Answer 1

To find the work done by the force field in moving a particle from one point to another, we use the fact that the force field is conservative (since it is derived from a potential function

). The work done is given by the negative change in the potential energy:

The potential function is given as:

### Step 1: Calculate

at \( (x, y, z) = (1, 1, 2) \)Substitute

,

, and

into \( U(x, y, z) \):

### Step 2: Calculate

at \( (x, y, z) = (2, 1, 2) \)Substitute

,

, and

into \( U(x, y, z) \):

### Step 3: Compute the work doneThe work done is:

### Final Answer:The work done by the force field is:

Soru

(c) A force field is given by the potential U=x^2+2y^2+z^3+2xy+2yz+z Find the work done by the force field in inoving a particle from the point (1,1,2) to (2,1,2) (3 marks)

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