Question

An air-track glider undergoes a perfectly inelastic collision with an identical glider that is initially at rest. what fraction of the first glider's initial kinetic energy is transformed into thermal energy in this collision?

Answer 1

Half of the first glider's initial kinetic energy is transformed into thermal energy in this collision.

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Further explanation

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.

$\large {\boxed {F = ma }$

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:

$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$

$mu + m(0) = mv + mv$

$mu = 2mv$

$u = 2v$

$\boxed {v = \frac{1}{2}u}$

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Next , we could calculate the change in kinetic energy of first glider:

$\Delta Ek : Ek_1 = ( Ek_1 - Ek ) : Ek_1$

$\Delta Ek : Ek_1 = ( \frac{1}{2}mu^2 - \frac{1}{2}(2mv^2)) : (\frac{1}{2}mu^2)$

$\Delta Ek : Ek_1 = ( mu^2 - 2mv^2 ) : (mu^2)$

$\Delta Ek : Ek_1 = ( mu^2 - 2m(\frac{1}{2}u)^2 ) : (mu^2)$

$\Delta Ek : Ek_1 = ( mu^2 - 2m(\frac{1}{4}u^2) ) : (mu^2)$

$\Delta Ek : Ek_1 = ( mu^2 - \frac{1}{2}mu^2 ) : (mu^2)$

$\Delta Ek : Ek_1 = ( \frac{1}{2}mu^2 ) : (mu^2)$

$\Delta Ek : Ek_1 = \frac{1}{2} : 1$

$\boxed {\Delta Ek = \frac{1}{2} Ek_1}$

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Conclusion:

Half of the first glider's initial kinetic energy is transformed into thermal energy in this collision.

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441
• Newton's Law of Motion: brainly.com/question/10431582
• Example of Newton's Law: brainly.com/question/498822

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

Answer 2

Refer to the diagram shown below.

The initial KE (kinetic energy) of the system is
KE₁ = (1/2)mu²

After an inelastic collision, the two masses stick together.
Conservation of momentum requires that
m*u = 2m*v
Therefore
v = u/2

The final KE is
KE₂ = (1/2)(2m)v²
       = m(u/2)²
       = (1/4)mu²
      = (1/2) KE₁

The loss in KE is
KE₁ - KE₂ = (1/2) KE₁.

Conservation of energy requires that the loss in KE be accounted for as thermal energy.

Answer:  1/2