A simple toy train set consists of two cars with a spring between them. The engine...

 

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A simple toy train set consists of two cars with a spring between them. The engine (first car) has a mass of 1.0 and the smaller one (the caboose) has a mass of 0.33 kg. The spring connecting them has a spring constant k-50 N/m. The spring is much lighter than either car, so you can consider it to have zero mass. A 5 N force is applied to the larger mass, in the forward direction. You can approximate the surface as frictionless and horizontal. a. Draw 3 separate free body diagrams, one for the engine and one for the caboose and one for the spring. b. Write down Newton's 2nd law for each car, one for the engine and one for the caboose, as well as for the spring. c. Explain from Newton's 2nd law on the spring why the force of the caboose on the spring is equal to the force of the engine on the spring (so that you can call both Fapring.) After an initial time to stretch the spring, the caboose and the engine should move together with the same acceleration. Find that acceleration a and the force of the spring Fepring d. e. Check that the acceleration you found in (d) agrees with what you would find by applying Newton's second law to the combined train system. A simple toy train set consists of two cars with a spring between them. The engine (first car) has a mass of 1.0 and the smaller one (the caboose) has a mass of 0.33 kg. The spring connecting them has a spring constant k-50 N/m. The spring is much lighter than either car, so you can consider it to have zero mass. A 5 N force is applied to the larger mass, in the forward direction. You can approximate the surface as frictionless and horizontal. a. Draw 3 separate free body diagrams, one for the engine and one for the caboose and one for the spring. b. Write down Newton's 2nd law for each car, one for the engine and one for the caboose, as well as for the spring. c. Explain from Newton's 2nd law on the spring why the force of the caboose on the spring is equal to the force of the engine on the spring (so that you can call both Fapring.) After an initial time to stretch the spring, the caboose and the engine should move together with the same acceleration. Find that acceleration a and the force of the spring Fepring d. e. Check that the acceleration you found in (d) agrees with what you would find by applying Newton's second law to the combined train system.

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