Kinetic energy lost in collision is 10 J.
Explanation:
Given,
Mass, [tex]m_{1}[/tex] = 4 kg
Speed, [tex]v_{1}[/tex] = 5 m/s
[tex]m_{2}[/tex] = 1 kg
[tex]v_{2}[/tex] = 0
Speed after collision = 4 m/s
Kinetic energy lost, K×E = ?
During collision, momentum is conserved.
Before collision, the kinetic energy is
[tex]\frac{1}{2} m1 (v1)^2 + \frac{1}{2} m2(v2)^2[/tex]
By plugging in the values we get,
[tex]KE = \frac{1}{2} * 4 * (5)^2 + \frac{1}{2} * 1 * (0)^2\\\\KE = \frac{1}{2} * 4 * 25 + 0\\\\[/tex]
K×E = 50 J
Therefore, kinetic energy before collision is 50 J
Kinetic energy after collision:
[tex]KE = \frac{1}{2} (4 + 1) * (4)^2 + KE(lost)[/tex]
[tex]KE = 40J + KE(lost)[/tex]
Since,
Initial Kinetic energy = Final kinetic energy
50 J = 40 J + K×E(lost)
K×E(lost) = 50 J - 40 J
K×E(lost) = 10 J
Therefore, kinetic energy lost in collision is 10 J.
