A 1500 kg car coasting on a horizontal road hits a 500 kg moose. The moose is thrown through the windshield into the passenger compartment. What percent of the initial kinetic energy is lost (turned into non-mechanical forms of energy) in the collision

% loss =K_{f}  / K₀ 100  =% 75%

Explanation:

This is a problem that we can solve using the conservation of the moment.

We define a system formed by the car plus the moose, so that the outside during the crash have been internal and the moment is preserved.

Initial moment. Before the crash

        p₀ = M v₁

Final moment. After the crash

      = (M + m) v

where M and m are the mass of the carra and the moose, respectively

       p₀ = p_{f}

       M v₁ = (M + m) v

        v = M / (M + m) v₁

now we can calculate the kinetic energy

before the crash

       K₀ = ½ M v₁²

after the crash

       K_{f} = ½ (M + m) v²

       K_{f} = ½ (M + m) (M / (M + m) v1)²

       K_{f} = ½ M² / (M + m) v₁²

In order to find a loss of energy, let's look for the relationship between the magnitudes

     % loss =K_{f}  / K₀ 100

     % loss = (½ M² / (M + m) v₁²) / ½ M v₁²   100

     % loss = M / (M + m) 100

     % loss = 1 / (1 + m / M) 100

     % loss = 1 / (1 + 500/1500) 100

     % loss = 75%

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