Final answer:
The work done by the force on the object as it moves from the origin to a specific point can be calculated using the formula: Work = Force · Displacement. Given the force F⃗ = 12 N i^ - 10 N j^ and the displacement r⃗ = 14 m i^ + 11 m j^, we can calculate the work to be 58 N·m.
Step-by-step explanation:
The work done by a force can be calculated using the formula:
Work = Force · Displacement
Given that the force is F⃗ = 12 N i^ - 10 N j^ and the object moves from the origin to the point r⃗ = 14 m i^ + 11 m j^, we can calculate the displacement:
Displacement = Final Position - Initial Position
Plugging in the values, we get Displacement = (14 m i^ + 11 m j^) - (0 m i^ + 0 m j^) = 14 m i^ + 11 m j^
Now, we can calculate the work:
Work = Force · Displacement = (12 N i^ - 10 N j^) · (14 m i^ + 11 m j^)
Using the dot product, we get:
Work = (12 N)(14 m) + (-10 N)(11 m) = 168 N·m - 110 N·m = 58 N·m