A constant force,
F = (4.63, −3.79, 2.16) N,
acts on an object of mass 17.7 kg, causing a displacement of that object by
r = (4.10, 3.86, −2.45) m.
What is the total work done by this force?
Im pretty sure the work equals -k(x-xo) but im not really sure what the values of r are supposed to be working here
4.63 * 4.10 work "in" in x direction
-3.79 * 3.86 work "out" in y direction (braking)
2.16 * -2.45 work "out" in z direction
now just add the results (not a vector)
4.63 * 4.10 - 3.79 * 3.86 - 2.16 * 2.45
Joules (scalar but does have sign)
To find the total work done by a force, we can use the formula:
W = F · r
Where W is the total work done, F is the force vector, and r is the displacement vector.
In this case, the force vector is given as F = (4.63, -3.79, 2.16) N, and the displacement vector is given as r = (4.10, 3.86, -2.45) m.
To calculate the work, we need to perform a dot product between the force vector and the displacement vector.
The dot product of two vectors is calculated by multiplying their corresponding components and summing the results. So, for our case, we have:
W = (F1 * r1) + (F2 * r2) + (F3 * r3)
W = (4.63 * 4.10) + (-3.79 * 3.86) + (2.16 * -2.45)
Now we can simply calculate the value of W by substituting the values:
W = 18.943 + (-14.643) + (-5.292)
W = -0.008 N.m
Therefore, the total work done by the force is approximately -0.008 N.m. It's important to note that work is a scalar quantity, and a negative value indicates that the force and displacement are in opposite directions.