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Your old toy train from pre-school days consists of three cars: M 1 = 0.2 kg, M

ID: 1432863 • Letter: Y

Question

Your old toy train from pre-school days consists of three cars: M1 = 0.2 kg, M2 = 0.4 kg, and M3 = 0.1 kg. You pull the cars with a force F = 4.5 N (red arrow in the picture). The coefficient of kinetic (rolling) friction between all three cars and the ground is ?k = 0.13.

What is the difference in the tensions between the two ropes, FTA - FTB?

Give your answer in Newtons to at least three significant digits to avoid rounding errors. Your answer will not be graded on the number of digits you provide.

M3 M2

Explanation / Answer

The data given in the question is,

mases M1 = 0.2 kg, M2 = 0.4 kg, and M3 = 0.1 kg

Total mass = 0.7kg.

force F = 4.5 N,The coefficient of kinetic (rolling) friction between all three cars and the ground is k = 0.13

What is the difference in the tensions between the two ropes, FTA - FTB=?
the friction force of all free cars is (m1 + m2 + m3)*g*0.1 = 0.7*9.81*0.13 = 0.8927 N
the friction force of cars 2+3 = (m2+m3)*g*0.13 = 0.6376 N
the friction force of car 3 is m3g*0.13 = 0.1275 N.
The net pulling force is F - Ffric = 4.5 - 0.8927 = 3.607N
The acceleration of the cars is Fnet/m = 3.607/0.7 = 5.15 m/s^2
The force necessary to accelerate car 3 at 5.15 m/s2is
F(3) = m3*a + friction force of m3
F3 = 0.1*5.15 + 0.1275 = 0.642 N = Tension in rope from car 2 to car 3
the force necessary to accelerate cars 2+3 at 5.13 m/s2 is
F(2,3) = 0.5*5.15 +0.6376= 3.212 N = Tension in rope from car 1 to car 2

FTA - FTB =3.212-0.642=2.570N