A child’s toy consists of three cars that are pulled in tandem on small frictionless rollers. The cars have masses m1=3.1 kg, m2 =2.4 kg, and m3 =1.2 kg....

Question

A child’s toy consists of three cars that are pulled in tandem on small frictionless rollers. The cars have masses m1=3.1 kg, m2 =2.4 kg, and m3 =1.2 kg. If they are pulled to the right with a horizontal force P = 6.5 N, find

(a) the acceleration of the system,

(b) the force exerted by the second car on the third car, and

(c) the force exerted by the first car on the second car.

Answer 1

The best way to do these problems is to draw a circle around the number of cars you want to consider as the system, and apply the second law. By choosing wisely, the problem is simplified and you need not solve simultaneous equations.

a) a = F_Net/m where the net force is just the pulling force to the right and the mass is the sum of the car masses. All the tensions are internal to the system, so they cannot move the three carts (They are 3rd law forces that cancel because they are internal to our system).

b) I don't think it is clear which car is being pulled on directly, but I'll assume it is m1. The third car will only have a force equal to the tension force of m2 on m3. Therefore,

F_2on3 = F_{net, 3} = m₃a but all the masses are accelerating with a from part a. You can solve for F.

c) You can solve this in many ways, but you can find the net force on m₂

F₁₂ - F₃₂ = m₂a | F₃₂ | = |F₂₃| from (b) and you know m₂ and a.

The really clever way is to treat m2 and m3 together to get the tension between 1 and 2.

F₁₂ = (m₂+m₃)a

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