Find the power input of a force
F=(7 N)ˆý + (3 N) ˆk acting on a particle that moves with a velocity
v = (6 m/s)ˆý.
Answer in units of W
I cant determine the vectors, but power= force dot velocity
To find the power input, we need to calculate the dot product between the force and velocity vectors. The dot product gives us the amount of work done by the force per unit of time, which is the definition of power.
The dot product of two vectors, A and B, is given by the formula: A · B = |A| |B| cos(theta), where |A| is the magnitude of vector A, |B| is the magnitude of vector B, and theta is the angle between the two vectors.
In this case, the force vector F = (7 N)ˆý + (3 N)ˆk and the velocity vector v = (6 m/s)ˆý.
Let's find the dot product:
F · v = (7 N)ˆý · (6 m/s)ˆý + (3 N)ˆk · (6 m/s)ˆý
To calculate the dot product, we only consider the components that are in the same direction, which is the y-direction. Therefore, we multiply the magnitudes of the components in the y-direction and the cosine of the angle between them, which is cos(0°) = 1:
F · v = (7 N) * (6 m/s) * cos(0°)
Now, we can plug in the values and evaluate the expression:
F · v = 7 * 6 * cos(0°)
Simplifying further, cos(0°) = 1, so:
F · v = 42 N m/s
Finally, power is defined as work done per unit time, so the power input (P) is equal to the dot product of force and velocity:
P = F · v = 42 N m/s
The unit of power is watts (W), so the answer is 42 W.