Answer:
5.4 J.
Explanation:
Given,
mass of the object, m = 2 Kg
initial speed, u = 5 m/s
mass of another object,m' = 3 kg
initial speed of another orbit,u' = 2 m/s
KE lost after collusion = ?
Final velocity of the system
Using conservation of momentum
m u + m'u' = (m + m') V
2 x 5 + 3 x 2 = ( 2 + 3 )V
16 = 5 V
V = 3.2 m/s
Initial KE = [tex]\dfrac{1}{2}mu^2 + \dfrac{1}{2}m'u'^2[/tex]
= [tex]\dfrac{1}{2}\times 2\times 5^2 + \dfrac{1}{2}\times 3 \times 2^2[/tex]
= 31 J
Final KE = [tex]\dfrac{1}{2} (m+m')V^2 = \dfrac{1}{2}\times 5 \times 3.2^2 = 25.6 J[/tex]
Loss in KE = 31 J - 25.6 J = 5.4 J.
Given values:
Mass of object,
Initial speed,
By using conservation of momentum,
→ [tex]mu = m'u' = (m+m') V[/tex]
By putting the values,
[tex]2\times 5+3\times 2=(2+3) V[/tex]
[tex]16=5 \ V[/tex]
[tex]V = \frac{16}{5}[/tex]
[tex]= 3.2 \ m/s[/tex]
Now,
The initial K.E will be:
= [tex]\frac{1}{2} mu^2+\frac{1}{2} m'u'^2[/tex]
= [tex]\frac{1}{2}\times 2\times 5^2+\frac{1}{2}\times 3\times 2^2[/tex]
= [tex]31 \ J[/tex]
The final K.E will be:
= [tex]\frac{1}{2} (m+m')V^2[/tex]
= [tex]\frac{1}{2}\times 5\times 3.2^2[/tex]
= [tex]25.6 \ J[/tex]
hence,
The loss in K.E will be:
= [tex]31-25.6[/tex]
= [tex]5.4 \ J[/tex]
Thus the above approach is right.
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