Kinetic Energy Question

[lucybug]

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I know this should be simple, but can someone explain why Kinetic Energy is not a vector. I know velocity is a vector. Thanks for the help.

KE= 1/2 mv^2.

 

[bluemonkey]

I know this should be simple, but can someone explain why Kinetic Energy is not a vector. I know velocity is a vector. Thanks for the help.

KE= 1/2 mv^2.

It's because you square the velocity vector. Either (-v)^2 or (v)^2 give the same result, thus the direction is lost in the squaring...

 

[iA-MD2013]

Yep, exactly what bluemonkey said...To generalize a little further, anytime you square a vector, you will end up with a scalar. You "lose direction" upon squaring a vector.

 

[Vihsadas]

Yup you guys are exactly right. If you want an intuitive explanation think of it this way:

If you stand in the middle of the road and throw a ball down the street, then turn around, and then throw the ball up the street with the same speed, is the kinetic energy different?

Nope, you imparted the same amount of energy on the ball regardless of the direction that you were tossing it. So, KE is not a vector.

 

[tncekm]

Yep, exactly what bluemonkey said...To generalize a little further, anytime you square a vector, you will end up with a scalar. You "lose direction" upon squaring a vector.

Yeah, to demonstrate that mathematically, usually '±i' is used for the x direction and '±j' is used for the y direction. If you square either of those quantities, they become i² and j², which says nothing of the direction!

 

[wannabedocta]

I just think of K.E. as work and I know work is definitely a scalar, so K.E. is probably also 😉