Another Work problem

[strugglin-physics]

A force F = (11.5i + 9.62j + 13.2k)kN acts on a small object of mass 109g. If the displacement of the object is d = (5.63i + 3.81j) m, calculate the work done by the force.

I know W=F*d*cos theta so W=101.4 cos theta
How do I find theta? Do I use the inverse tangant of the F and the d?

[kenhcm]

The work done is defined by the dot product (or inner product) between the force vector and the displacement vector. In the cartesian coordinate system, we have

W = F_x*d_x + F_y*d_y + F_z*d_z

where F_x is the x-component of the force, d_x is the x-component of the displacement and similarly for others.

Best regards,
Kenneth

[strugglin-physics]

Right, got that part, I think.
W=11.5*5.63 + 9.62*3.81 + 13.2*0 = 101.4 cos theta
My question is how to find theta. would theta be the inverse tangant of 36.65/64.75?

[Doc Al]

Right, got that part, I think.
W=11.5*5.63 + 9.62*3.81 + 13.2*0 = 101.4 cos theta
My question is how to find theta. would theta be the inverse tangant of 36.65/64.75?
W=11.5*5.63 + 9.62*3.81 + 13.2*0 = 101.4, not 101.4 cos (theta)!

There are (at least) two ways to calculate work, depending upon what you are given:

(1) W = F*d*cos(theta), is good if you are given the magnitude of the force and displacement and the angle between them.

(2) W = F_x*d_x + F_y*d_y + F_z*d_z, is good if you are given the components.

When you use method #2, theta is not needed.

[strugglin-physics]

It says that the answer is not 101.4

And the next questions says What is the angle between F and d?

[Doc Al]

It says that the answer is not 101.4
Check the units. The force was given in kN.

And the next questions says What is the angle between F and d?
If you know W, F, and d, then you can find theta using W = Fd cos(theta). F and d are the magnitudes of the vectors.

[strugglin-physics]

Ahh that makes sense. I was trying to figure it out without first finding the work. Thanks