Question

A 1.00 kg object moving in the + x direction at 10.0 m/s collides with a 1.50 kg object traveling at 5.00 m/s in the - x direction. After the collision, the 1.00 kg object moves with a velocity of 4.00 m/s in the - x direction. How much kinetic energy was lost during the collision?

Answer 1

The amount of kinetic energy lost during the collision is 60.75 J

Step-by-step explanation:

The given parameters are;

The mass of the object moving in the +x direction, m₁ = 1.00 kg

The velocity of the object moving in the +x direction, v₁ = 10.0 m/s

The mass of the object moving in the -x direction, m₂ = 1.50 kg

The velocity of the object moving in the +x direction, v₂ = 5.00 m/s

The final velocity of the 1.00 kg mass after collision, v₃ = 4.00 m/s

The direction of motion of the 1.00 kg mass after collision = -x direction

The total initial kinetic energy of the system,
`K.E._(total \ initial)` = 1/2·m₁·v₁² + 1/2·m₂·v₂²

∴
`K.E._(total \ initial)` = 1/2×1.00×10² + 1/2×1.50×5² = 68.75 J

The final kinetic energy of the system,
`K.E._(final)` = 1/2·m₁·v₃²

`K.E._(final)` = 1/2×1.00×4² = 8 J

The amount of kinetic energy lost during the collision,
`\Delta K.E._(system)` is given as follows;

`\Delta K.E._(system)` =
`K.E._(final)` -
`K.E._(total \ initial)` = 8 J - 68.75 J = -60.75 J

The amount of kinetic energy lost during the collision = 60.75 J.