A barge with a mass 1.75×10 5 kg is proceeding down river at 6.00 m/s in heavy f

ID: 1695767 • Letter: A

Question

A barge with a mass 1.75×105kg is proceeding down river at 6.00 m/s in heavy fog when it collides with a barge heading directly across the river as in the figure. The second barge has mass 1.90×105kg and is moving at 5.00 m/s.

Immediately after impact, the second barge finds its course deflected by an angle of 18.0° in the downward direction and its speed increased to 5.10 m/s. The river current was practically zero at the time of the accident. What is the speed of the first barge immediately after the collision?

How much kinetic energy is lost in the collision?

Explanation / Answer

according to law of conservation of energy,

the total energy of the before collision = the total energy of after the collision (independent of the angle)

1/2 m1u1^2 + 1/2 m2u2^2 = 1/2m1v1^2 + 1/2 m2v2^2

1.75*10^5 *36 + 1.90*10^5*25 = 1.75*10^5*V2^2 + 1.9*10^5*(5.10)^2

110.5*10^5 - 49.41*10^5 = 1.75*10^5*V2^2

V2^2 = 34.6

V2 = 5.88 m/s

the speed of the first barge immediately after the collision is 5.88 m/s.

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A barge with a mass 1.75×10 5 kg is proceeding down river at 6.00 m/s in heavy f

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