A light and a heavy body have equal momenta. Which one has greater kinetic enerty? (a) The heavy

step 1 we have the number 46 in which there are two blocks let us suppose this is a smaller block that

A light and a heavy body have equal momenta. Which one has...

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Key Concepts

Momentum

Momentum is a vector quantity defined as the product of an object's mass and its velocity. It determines how difficult it is to stop a moving object, and it is conserved in isolated systems. This principle lays the groundwork for analyzing motion when comparing different bodies with varied masses and velocities.

Kinetic Energy

Kinetic energy is a scalar quantity that measures the energy an object possesses due to its motion. It is given by the equation KE = 1/2 mv². This concept helps in understanding the work done by or against forces acting on objects in motion.

Dependence on Mass

The contributions of mass to momentum and kinetic energy are different. While momentum increases linearly with mass for a given velocity, kinetic energy increases with the square of the velocity. This means that for two objects with the same momentum, the one with a smaller mass must have a higher velocity, which in turn increases its kinetic energy significantly.

Relationship Between Momentum and Kinetic Energy

For a given momentum, kinetic energy can be expressed as KE = p²/(2m). This inverse relationship with respect to mass implies that a lighter object (with smaller mass) will have higher kinetic energy compared to a heavier object when both have the same momentum.

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