Answer:
(a) K₁ = 2.205 J.
(b) K₂ = 5.733 J.
(c) K₂/K₁ = 2.6.
Step-by-step explanation:
Kinetic Energy: This can be defined as the energy of a body in motion. The Unit of kinetic energy is J.
Mathematically kinetic energy can be represented as,
K = 1/2mv²
(a)
K₁ = 1/2m₁v₁²............................ Equation 1
Where K₁ = kinetic energy of the smaller bullet, m₁ = mass of the smaller bullet, v₁ = velocity of the smaller bullet.
Given: m₁ = 2.5 g = 2.5/1000 = 0.0025 kg, v = 42 m/s.
Substituting these values into equation 1
K₁ = 1/2(0.0025)(42)²
K₁ = 4.41/2
K₁ = 2.205 J.
(b)
K₂ = 1/2m₂v₂²............................. Equation 2
Where K₂ = kinetic energy of the heavier bullet, m₂ = mass of the heavier bullet, v₂ = velocity of the heavier bullet.
Given: m₂ = 6.5 g = 6.5/1000 = 0.0065 kg, v₂ = 42.0 m/s
Substituting into equation 2,
K₂ = 1/2(0.0065)(42)²
K₂ = 11.466/2
K₂ = 5.733 J.
(c)
The ratio: K₂/K₁ = 5.733/2.205
K₂/K₁ = 2.6.