Force Vector into a Force (Power)

[Havok23]

Homework Statement

Find the power input of a force vector F acting on a particle that moves with a velocity vector v for each of the following situations.
(a) vector F = 4 N i hat + 3 N k hat , vector v = 9 m/s i hat

Homework Equations

P = F * V

The Attempt at a Solution

P =(4*9) +3

Also tried

P = SQRT(4^2+3^2) * 9
I guess the problem is I don't know how to convert the vector 4i+3j into a force.

 

[G01]

That vector is the force. You have a force with an x component of 4N and a y component of 3N.

In order to find the power you need to find the dot product of F and v:

[tex]P=\vec{F}\cdot\vec{v}=F_xv_x+F_yv_y[/tex]

It seems like this was what you were trying to do in your first attempt. You made one small mistake. HINT: What is [itex]v_y[/itex]?

 

[baba89]

I would like to clarify that a force vector is already a force, it is just represented in a vector form. Therefore, there is no need to convert it into a force. The vector 4N i hat + 3N k hat represents a force of 4N in the x-direction and 3N in the z-direction.

To find the power input, we can use the equation P = F * V, where P is the power, F is the force, and V is the velocity. In this case, the force vector F = 4N i hat + 3N k hat and the velocity vector v = 9 m/s i hat.

Substituting these values into the equation, we get:

P = (4N i hat + 3N k hat) * (9 m/s i hat)

= (4N * 9 m/s) + (3N * 0 m/s)

= 36 W + 0 W

= 36 W

Therefore, the power input of the force vector F on the particle is 36 Watts.