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The engine of a train has a mass of 5x10^4 kg. it can accelerate six railway cars having a total mass of 3x10^5 kg by 0.4 m/s^2 (the 6 railway cars have a combined mass of 3x10^5). what acceleration can the same engine using the same force give to four railway cars having a total mass of 2x10^5kg?

it is proportional inversely

a1/a2=M2/M1

a1/a2=(3E5+5E4)/(2E5+5E4)
solve for a1 in terms of the original a2 acceleration.

let us examine it:

let F be the pulling force, mu the coefficent of friction.
Net pulling force= totalmass*a
F-mu(totalmass)=totalmass*a
F= totalmass(a+mu)

but F the pulling force remains the same on both trains

so

totalmass1(a1+mu)=totalmass2(a2+mu)

TM1*a1+ TM1*mu=TM2*a2+TM2*mu
a2= (TM1*a1+TM1*mu-TM2*mu)/TM2

in case one, TM1= 5E4+3E5, and in case two, TM2=(5E4+2E5)

Your teacher did not specific the friction. If you ignore friction, mu=0, but mu is hardly ever even close to zero on a freight train.

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