Question

If two objects one with mass0.5 having velocity 2 and other mass 1 having velocity 1 moving on frictionless surface and after colliding stick together what is there kinetic energy

Answer 1

Explanation:

R.E.F image

By momentum conservation

0.5×2=1.5×v

v=

3

2

m/sec

Initial Energy =

2

1

×0.5×(2)

2

=1 joule .

Final Energy =

2

1

×1.5×(

3

2

)

2

=1/3 joule .

Loss= Initial-Final

=1−

3

1

=

3

2

=0.67J

Answer 2

Given :

• Mass of A(m) = 0.5
• Velocity of A (u)= 2 m/s
• Mass of B (m')= 1 kg
• Velocity of B(u') = 1 m/s

To find :

• Final kinetic energy

How to solve :

• First we need to find the velocity of the combined mass after collision . In order to do that simply use law of conservation of energy as no external force was acting on the system so the energy remains conserved .

• Then , simply substitute the value of v in the formula to find kinetic energy .

Solution :

As per law of conservation of energy ,

Initial Energy = Final energy

$\implies\mathtt{ KE_ a + KE_ b = KE_ f }$

⇒ m x u² / 2 + m' x u' ²/ 2 = (m +m' ) v ²/ 2

⇒ m x u² + m' x u' ² = (m +m' ) v ²

⇒ 0.5 x 4 + 1 x 1 = 1.5 v²

⇒ 2 + 1 = 1.5 v²

⇒ v²= 3 / 1.5

⇒ v² = 2

Now that we have the value of v , let us find the final kinetic energy of the combined mass .

⇒ KE f =(m + m' ) v² / 2

⇒ KE f = (1 +0.5 ) x 2 / 2

⇒ KE f = 1.5 J

The kinetic energy of the combined mass after collision is 1.5 J .