Derive an expression for the Kinetic energy of an object moving with velocity ‘v’ and the mass of an object becomes half of its original mass. Useless answers will be reported. Please show how you derived.
Answers
Answer:-
The required expression is :-
K.E.' = ¼mv²
Explanation:-
We know that :-
K.E. = ½mv²
Where :-
• K.E. is kinetic energy of the body.
• m is mass of the body.
• v is velocity of the body.
In this case, mass of the object becomes half of its original mass i.e. m/2.
Thus, the expression of new kinetic energy [K.E'] becomes :-
⇒K.E.' = 1/2 × m/2 × v²
∴ K.E' = ¼mv²
Some Extra Information:-
• Kinetic energy is the energy possessed
by a body because of it's motion. It is a
scalar quantity.
• Kinetic energy of a body depends on
two factors :-
(a) Mass [K.E. ∝ m]
(b) Velocity [K.E. ∝ v²]
• Kinetic energy of a body is always
positive. This is beacuse mass can
never be negative and square of a real
value is always positive.
Let, mass of the object (initial) = M
Velocity of the particle = v
∴ Initial KE = ½Mv²
[∵ KE formula = ½ × (mass) × (velocity)²]
But now,
Final mass = M/2
∴ Final KE = ½(M/2)v² = Mv²/4 = ¼Mv² (answer).