A constant force -6i-2j-1k moves an object along a straight line from point (8, -6, -9) to point (-5, 3, 3).
how do you find the work done
Take the scalar "dot" product of the force vector and the displacement vector. The displacement vector is
-13i +9j +12k
(-13)*(-6) + 9*(-2) + 12*(-1)
= ?
To find the work done by a constant force, you can use the formula:
Work = Force dot Product Displacement
Where,
- Force is the constant force acting on the object.
- Displacement is the change in position of the object.
In this case, the constant force is given as -6i - 2j - 1k, and the displacement is the change in position from point (8, -6, -9) to point (-5, 3, 3).
1. Find the displacement vector:
The displacement vector can be obtained by subtracting the initial position vector from the final position vector.
Displacement = Final position - Initial position
Displacement = (-5 - 8)i + (3 - (-6))j + (3 - (-9))k
Displacement = -13i + 9j + 12k
2. Calculate the dot product of the force and displacement vectors:
To compute the dot product, multiply the corresponding components of both vectors and sum them up.
Force dot Product Displacement = (-6)(-13) + (-2)(9) + (-1)(12)
Force dot Product Displacement = 78 - 18 - 12
Force dot Product Displacement = 48
Therefore, the work done by the constant force is 48 units.