Your old toy train from preschool days consists of three car

Your old toy train from pre-school days consists of three cars: M1 = 0.3 kg, M2 = 0.4 kg, and M3 = 0.1 kg. You pull the cars with a force F = 3.0 N (red arrow in the picture). The coefficient of kinetic (rolling) friction between all three cars and the ground is k = 0.11. 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.

Solution

Total mass = 0.3 + 0.4 + 0.1 = 0.8 kg

Friction = (0.8 * 9.8) * 0.11 = 0.86 N

acceleration Force = F - f_f = 3.0 - 0.86 = 2.14 N

a = f / m = 2.14 / 0.8 = 2.675 m/s²

F_TA = m a = (0.4 + 0.1) * 2.675 = 1.34 N

F_TB = m a = 0.1 * 2.675 = 2.675 N

difference in the tensions between the two ropes

= 1.34 N