Work — Question 2

Question 2

A constant force ignores the route but not the endpoints

For a constant force, use $W=\vec F\cdot\Delta\vec r$. A constant force $(4,-3)$ N acts while a particle goes from O=(0,0) to B=(3,2) m. Route I is straight; route II goes first to A=(3,0), then to B.

1. Find work on route I.

2. Find work on each leg of route II and the total.

3. Find work by this same force on the return straight from B to O, and on the complete loop.

Question 2 - Solution

A constant force ignores the route but not the endpoints

(a) Use total displacement.

The governing relation is $$\boxed{W_{if}=F_x(x_f-x_i)+F_y(y_f-y_i)}$$

$$W_I=4(3)-3(2)=6\ \mathrm J.$$

(b) Add signed segment contributions.

O to A gives 12 J; A to B gives $-6\ \mathrm J$. The total is 6 J because the constant force can be factored out of the sum of displacement vectors.

(c) Reverse the endpoint difference.

Return work is $-6\ \mathrm J$ and loop work is zero. The traveled distance is nonzero on the loop, but $$\sum\Delta\vec r=0$$ for this unchanged force.