A constant force, F = (4.39, −3.79, 2.02) N, acts on an object of mass 19.5 kg, causing a displacement of that object by r = (4.02, 3.68, −2.45) m. What is the total work done by this force?
work = force * distance
so, calculate |F| and |r| and multiply
To calculate the total work done by a force, you can use the formula: W = F * d * cos(theta), where F is the force vector, d is the displacement vector, and theta is the angle between the force and displacement vectors.
First, let's calculate the dot product of the force vector (F) and the displacement vector (r). The dot product of two vectors is given by the formula: A · B = (Ax * Bx) + (Ay * By) + (Az * Bz), where Ax, Ay, and Az are the components of vector A, and Bx, By, and Bz are the components of vector B.
So, let's calculate the dot product of F and r:
F · r = (4.39 * 4.02) + (-3.79 * 3.68) + (2.02 * -2.45).
Now, let's calculate the magnitude of F:
|F| = sqrt(Fx^2 + Fy^2 + Fz^2), where Fx, Fy, and Fz are the components of F.
Finally, let's calculate the angle between F and r:
cos(theta) = (F · r) / (|F| * |r|), where |F| is the magnitude of F, and |r| is the magnitude of r.
Now that we have all the necessary values, we can calculate the total work done:
W = F * d * cos(theta).
Let's plug in the known values into the formula and perform the calculations to find the total work done.