Physics: Conservation of momentum
Physics

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Three identical train cars, coupled together, are rolling east at 1.5
what is the speed of the 4 car train ?
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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.
How would I solve for this portion of the problem>
The fourcar train rolls down the track without losing speed until they collide with and couple to a fifth car that is stationary on the train tracks. If the fifth car is identical to other four, what is the speed of the fivecar train?
Use the same formula for before and after the collision
Without retyping and plugging in it looks like this...
4m(9/8)+m(0)=(4m+m)v
36m/8m=5mv Divide by 5m.
36/40=v Reduce the fraction and make it a decimal. Can be done with a calculator 36/40=.9
.9=v This is the velocity of the 5 car train.
I am doing my homework online and it says that this answer is incorrect
Sorry. There was something wrong with your post. There was information missing. But I see it now.
The 4th car originally is moving at 4.2 not 0.
3m(1.5)+m(4.2)=(3m+m)v
4.5m+4.2m=4mv
8.7m=4mv Divide by 4m
8.7m/4m=v
2.175=v
Use 2.175 instead of 9/8 in the other equation.
4m(2.175)+m(0)=(4m+m)v It is 0 because the fifth car is stationary aka not moving.
8.7m=5mv Divide by 5m.
8.7m/5m=v
1.74=v
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