If the KE and momentum of a body are 100 J and 20 kg m s^-1 respectively, the mass of the bo

step 1 problem number 13 in which we have been given the kinetic energy and momentum of a body so kinet

If the KE and momentum of a body are 100 J and 20 kg m...

If the $\mathrm{KE}$ and momentum of a body are $100 \mathrm{~J}$ and $20 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}$ respectively, the mass of the body is
(a) $1 \mathrm{~kg}$
(b) $2 \mathrm{~kg}$
(c) $3 \mathrm{~kg}$
(d) $4 \mathrm{~kg}$

Key Concepts

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion. It is calculated using the formula KE = ½ * m * v², where m is the mass and v is the velocity of the object. This concept is fundamental in mechanics as it relates the movement of an object to the work it can perform.

Momentum

Momentum is a measure of the quantity of motion of an object and is defined as the product of its mass and velocity (p = m * v). It is a vector quantity, meaning it has both magnitude and direction, and it plays a key role in understanding the behavior of moving bodies and collisions.

Relationship Between Kinetic Energy and Momentum

The relationship between kinetic energy and momentum can be established by expressing velocity in terms of momentum and mass. Substituting v = p/m into the kinetic energy formula leads to an expression KE = p²/(2m). This relation is particularly useful for solving problems where kinetic energy and momentum are known, allowing for the determination of the mass of an object.

Algebraic Manipulation

Algebraic manipulation involves rearranging and solving equations to isolate and determine unknown variables. In the context of mechanics, using algebra to rearrange the kinetic energy and momentum formulas allows one to derive relationships between different physical quantities, such as solving for mass when both kinetic energy and momentum are provided.

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