Solve the problem.
-A constant force $F = 13 i + 26 j$ moves an object from the point $P = ( 5,2 )$ to the point $Q = ( 3,15 )$, where units are in pounds and feet. Find the work done.
A) $- 13$ foot-pounds
B) 13 foot-pounds
C) 117 foot-pounds
D) $156.5$ foot-pounds

Question

Quizplus · Accepted Answer

The work done by a force during a displacement is given by the dot product of the force vector and the displacement vector. The displacement vector $\Delta r$ from point $P$ to point $Q$ is $\Delta r = Q - P = (3 - 5, 15 - 2) = (-2, 13)$. The force vector $F$ is $13i + 26j$. The work done $W$ is the dot product of $F$ and $\Delta r$, which is $W = F \cdot \Delta r = (13)(-2) + (26)(13) = -26 + 338 = 312$ foot-pounds.

Solve the Problem F=13i+26jF = 13 i + 26 jF=13i+26j Moves an Object from the Point

Solve the Problem $F = 13 i + 26 j$ Moves an Object from the Point