Physics: Conservation of momentum

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royngpuebq

Science

Description

Three identical train cars, coupled together, are rolling east at 1.5 

m/s . A fourth car traveling east at 4.2 m/s catches up with the three and couples to make a four-car train.

what is the speed of the 4 car train ?

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Explanation & Answer

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m_1*v_1+m_2v_2=(m_1+m_2)v_3     The left side of the equation is 3 car momentum added to the 1 car momentum before the collision. The right side of the equation is the momentum of all 4 cars after the collision. Momentum=mv for any object.

The space _ denotes sub 1,2, or 3 to show which object it is.

If the first three trains have mass 3m because each one has mass m. These represent mass number 1. It is a variable since we do not know its actual mass. They have a velocity of 1.5. The second train or mass number 2 is just m because it is identical to the other three train cars. This car has velocity 0 because it is not moving at the beginning of the problem. The equation can now be filled in to solve for the third velocity aka the 4 car train.

(3m)(1.5)+(m)(0)=(3m+m)v_3 I plugged in for what I know.

4.5m+0=4m(v_3) I simplified by putting terms together.

4.5m=4m(v_3) I dropped the 0. Now divide by 4m.

9/8=v_3 This is the final velocity of all the masses combined at the time after the collision when the 4 car train is moving.

Please let me know if you need any clarification. I'm always happy to answer your questions.

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