Q8DQ - University Physics with Modern Physics

Question

In Example 8.7 (Section 8.3), where the two gliders ofFig. 8.18 stick together after the collision, the collision is inelastic because ${\mathit{K}}_{\mathbf{1}}\mathbf{<}{\mathit{K}}_{\mathbf{2}}$ . In Example 8.5 (Section 8.2), is the collisioninelastic? Explain

Step-by-Step Solution

Answer

The kinetic energy before the collision is more than after the collision, therefore collision is inelastic.

Step 1: Given information in the Example 8.5 (Section 8.2)

Mass of glider A, $m_A=0.50kg$

The initial velocity of glider A, $v_{A1}=2.0m/s$

The final velocity of glider A, $v_{A2}=-0.40m/s$

 

Moss of glider B, $m_B=0.30kg$

The initial velocity of glider B, $v_{B1}=-2.0m/s$

The final velocity of glider B, $v_{B2}=2.0m/s$

Step 2: Definition of collision

When two moving bodies or one moving body and one at rest collide, this is referred to as a collision.

Step 3: Discussion.

The kinetic energy of an object is given by,

 

$K=\frac{1}{2}m{v}^2$

 

The total kinetic energy of the system of two gliders before the collision is given as.

 

$$\begin{gathered} K_1=K_{A1}+K_{B1} \\ =\frac{1}{2}{m}_A{v^2}_{Al}+\frac{1}{2}{m}_B{v^2}_{Bl} \\ =\frac{1}{2}\left(0.50kg\right){\left(2.0m/s\right)}^2+\frac{1}{2}\left(0.30kg\right){\left(-2.0m/s\right)}^2 \\ =1.6 J \end{gathered}$$

 

The total kinetic energy of the system of two gliders after the collision is given as

 

$$\begin{gathered} K_2=K_{A2}+K_{B2} \\ =\frac{1}{2}{m}_A{v^2}_{A2}+\frac{1}{2}{m}_B{v^2}_{B2} \\ =\frac{1}{2}\left(0.5kg\right){\left(0.4m/s\right)}^2+\frac{1}{2}\left(0.3kg\right){\left(2.0m/s\right)}^2 \\ =0.64J \end{gathered}$$

 

Since $K_1>K_2$ , this implies the kinetic energy before collision is more than after the collision, therefore collision is inelastic.