# Kinetic Energy Not Necessarily Equal w/ Same Momentum

• rmarkatos
In summary, momentum and kinetic energy are not necessarily the same for two objects with the same momentum. They both depend on mass and velocity, but momentum is a vector quantity while kinetic energy is a scalar quantity. This can be seen through examples where the momentums are not equal but the kinetic energies are, or when the momentums are equal but the kinetic energies are not.
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

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.

Last edited:

While both formulas include mass and velocity, the way they are calculated is different. Momentum is calculated by multiplying the mass and velocity, while kinetic energy is calculated by multiplying the mass, velocity, and an additional factor of 1/2. This means that even if two objects have the same momentum, their kinetic energy will not necessarily be equal because the additional factor of 1/2 can make a significant difference in the final calculation. Therefore, two objects with the same momentum can have different kinetic energies.

## What is kinetic energy?

Kinetic energy is the energy that an object possesses due to its motion. It is a scalar quantity and is dependent on the mass and velocity of an object.

## What is momentum?

Momentum is a measure of an object's motion, calculated by multiplying its mass and velocity. It is a vector quantity and is conserved in a closed system.

## Can two objects have the same momentum but different kinetic energy?

Yes, two objects can have the same momentum but different kinetic energy. This can occur if one object has a greater mass but a lower velocity compared to the other object.

## Why is kinetic energy not necessarily equal to momentum?

Kinetic energy and momentum are two different quantities that measure different aspects of an object's motion. Kinetic energy takes into account an object's mass and velocity, while momentum only considers an object's mass and speed.

## Can an object have zero kinetic energy but non-zero momentum?

Yes, an object can have zero kinetic energy but non-zero momentum. This can happen if an object is at rest (zero velocity) but has a non-zero mass. The object still possesses momentum due to its mass, but it does not have any kinetic energy because it is not in motion.

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