Power of Energy Transfer: Solving a 3D Vector Problem

[eraemia]

Homework Statement

An object moves with a velocity of [4 m/s,-1 m/s, 3 m/s] and is acted on by a force of [-5 N, 0, +5 N]. What is the power of the energy transfer in this interaction?

a. -35 W
b. -5 W
c. 0
d. +5 W
e. +35 W

Homework Equations

p = Fv

The Attempt at a Solution

Okay, so I'm trying to find p, and I'm given Fv, and I know that p = Fv. The problem is that it's invalid to multiply these two matrices. So what do I do? I don't know how to multiply these two three-dimensional vectors? What do I need to do first?

 

[dynamicsolo]

Homework Statement

An object moves with a velocity of [4 m/s,-1 m/s, 3 m/s] and is acted on by a force of [-5 N, 0, +5 N]. What is the power of the energy transfer in this interaction?

a. -35 W
b. -5 W
c. 0
d. +5 W
e. +35 W

Homework Equations

p = Fv

The Attempt at a Solution

Okay, so I'm trying to find p, and I'm given Fv, and I know that p = Fv. The problem is that it's invalid to multiply these two matrices. So what do I do? I don't know how to multiply these two three-dimensional vectors? What do I need to do first?

Have you learned about how to take the dot product between two vectors in component notation? I suspect that's the approach you're expected to take, given the choice of these vectors in three dimensions... (BTW, P = F·v is a better way to write the equation for this sort of problem.)

 

[m2003]

I would first clarify the units of each vector component. The velocity is given in meters per second, while the force is given in Newtons. In order to calculate power, which is measured in watts, we need to use a unit conversion factor to ensure that the units are consistent. In this case, we can use the definition of a watt, which is equal to one joule per second.

Next, we can use the dot product formula to find the power of the energy transfer. The dot product of two vectors is equal to the product of their magnitudes multiplied by the cosine of the angle between them. In this case, the angle between the force and velocity vectors is 90 degrees, so the cosine of the angle would be 0. Therefore, the power of the energy transfer would be equal to the magnitude of the force vector (5 N) multiplied by the magnitude of the velocity vector (4 m/s), which gives us a power of 20 watts.

In summary, to solve this 3D vector problem, we first need to convert the units to ensure consistency, and then use the dot product formula to calculate the power of the energy transfer. This is an important skill for scientists, as many real-world problems involve multiple vectors and require a clear understanding of vector operations.