How will the momentum of a body change if its kinetic energy is doubled?
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Kinetic energy = (Momentum)² / (2 × mass)
K = p² / (2m)
K₂/K₁ = (p₂/p₁)²
p₂/p₁ = √(K₂/K₁)
p₂/p₁ - 1 = √(K₂/K₁) - 1
Δp/p₁ = √(K₂/K₁) - 1
Δp = p₁ × √(K₂/K₁) - 1
Δp = p₁ × √(2K₁/K₁) - 1
Δp = 0.414p₁
%Change in momentum = 0.414 × 100 = 41.4%
Momentum will increase by 41.4%
K = p² / (2m)
K₂/K₁ = (p₂/p₁)²
p₂/p₁ = √(K₂/K₁)
p₂/p₁ - 1 = √(K₂/K₁) - 1
Δp/p₁ = √(K₂/K₁) - 1
Δp = p₁ × √(K₂/K₁) - 1
Δp = p₁ × √(2K₁/K₁) - 1
Δp = 0.414p₁
%Change in momentum = 0.414 × 100 = 41.4%
Momentum will increase by 41.4%
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