Half of the first glider's initial kinetic energy is transformed into thermal energy in this collision.
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Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.
[tex]\large {\boxed {F = ma }[/tex]
F = Force ( Newton )
m = Object's Mass ( kg )
a = Acceleration ( m )
Let us now tackle the problem !
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Given:
mass of first glider = m₁ = m
mass of second glider = m₂ = m
initial speed of first glider = u₁ = u
initial speed of second glider = u₂ = 0
final speed of both gliders = v₁ = v₂ = v → perfectly inelatic collision
Asked:
change in kinetic energy = ΔEk = ?
Solution:
Firstly , we will use Conservation of Momentum Law as follows:
[tex]m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2[/tex]
[tex]mu + m(0) = mv + mv[/tex]
[tex]mu = 2mv[/tex]
[tex]u = 2v[/tex]
[tex]\boxed {v = \frac{1}{2}u}[/tex]
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Next , we could calculate the change in kinetic energy of first glider:
[tex]\Delta Ek : Ek_1 = ( Ek_1 - Ek ) : Ek_1[/tex]
[tex]\Delta Ek : Ek_1 = ( \frac{1}{2}mu^2 - \frac{1}{2}(2mv^2)) : (\frac{1}{2}mu^2)[/tex]
[tex]\Delta Ek : Ek_1 = ( mu^2 - 2mv^2 ) : (mu^2)[/tex]
[tex]\Delta Ek : Ek_1 = ( mu^2 - 2m(\frac{1}{2}u)^2 ) : (mu^2)[/tex]
[tex]\Delta Ek : Ek_1 = ( mu^2 - 2m(\frac{1}{4}u^2) ) : (mu^2)[/tex]
[tex]\Delta Ek : Ek_1 = ( mu^2 - \frac{1}{2}mu^2 ) : (mu^2)[/tex]
[tex]\Delta Ek : Ek_1 = ( \frac{1}{2}mu^2 ) : (mu^2)[/tex]
[tex]\Delta Ek : Ek_1 = \frac{1}{2} : 1[/tex]
[tex]\boxed {\Delta Ek = \frac{1}{2} Ek_1}[/tex]
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Half of the first glider's initial kinetic energy is transformed into thermal energy in this collision.
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Grade: High School
Subject: Physics
Chapter: Dynamics
