Kinetic Energy Not Necessarily Equal w/ Same Momentum

[rmarkatos]

Conceptual Question

If two objects have the same momentum do they necessarily have the same kinetic energy? Give your reason.

I would say no basically from just looking at formulas.

P=mv for momentum

K.E.= 1/2mv^2 for kinetic energy

 

[radou]

Of course momentum is not the same as kinetic energy. But momentum and kinetic energy both depend on two variables; the mass and the velocity. Also, note that momentum is a vector quantity, while kinetic energy is a scalar quantity.

Edit: look at this example. Let $$\vec{p}_{1} = m \vec{v}_{1}$$, and $$\vec{p}_{2} = m \vec{v}_{2}$$, where $$\vec{v}_{1} = 3 \vec{i}$$, $$\vec{v}_{2} = 3 \vec{j}$$. The momentums are not the same (the magnitudes are, but the directions are not), and the kinetic energies are the same.

Or, you can look at s non-vector example (assume both momentums are in the same direction): let the momentum be equal, so that m1v1 = m2v2. For example, you can take m1 = 3, and v1 = 4, and m2 = 4, and v2 = 3. Now try to calculate the kinetic energies and see in what relation they are.