HW 4.1: Accelerating Systems (pg. 2 of 2) Q2 Train Example: A train engine pulls a train with three cars. Each car has the mass shown. Suppose that the cars are connected by ropes with the tensions indicated in the diagram. The engine accelerates at a rate of 2 m/s². Assume that the cars travel on frictionless bearings. 3000 kg 2000 kg 1000 kg (a) On the dots below, draw free-body diagrams showing the forces acting on each of the three train cars. For each diagram, write an equation that relates the forces in the diagram to acceleration. Forces on the 3000 kg car Forces on the 2000 kg car Forces on the 1000 kg car 10-9 (b) On the squares below, draw external force diagrams showing only the external forces acting on each of the systems indicated. Please omit forces that balance. For each diagram, write an equation that relates the forces in the diagram to acceleration. Forces on the 2000-1000 system Forces on 3000-2000-1000 system Forces on the 3000-2000 system (c) Use the equations you wrote above to find each of the three tensions T1, T2, and T3. (d) Without referencing any math or any numbers, explain why Ti is the greatest tension and T3 is the weakest tension, even though T3 is connected to the greatest mass.
HW 4.1: Accelerating Systems (pg. 2 of 2) Q2 Train Example: A train engine pulls a train with three cars. Each car has the mass shown. Suppose that the cars are connected by ropes with the tensions indicated in the diagram. The engine accelerates at a rate of 2 m/s². Assume that the cars travel on frictionless bearings. 3000 kg 2000 kg 1000 kg (a) On the dots below, draw free-body diagrams showing the forces acting on each of the three train cars. For each diagram, write an equation that relates the forces in the diagram to acceleration. Forces on the 3000 kg car Forces on the 2000 kg car Forces on the 1000 kg car 10-9 (b) On the squares below, draw external force diagrams showing only the external forces acting on each of the systems indicated. Please omit forces that balance. For each diagram, write an equation that relates the forces in the diagram to acceleration. Forces on the 2000-1000 system Forces on 3000-2000-1000 system Forces on the 3000-2000 system (c) Use the equations you wrote above to find each of the three tensions T1, T2, and T3. (d) Without referencing any math or any numbers, explain why Ti is the greatest tension and T3 is the weakest tension, even though T3 is connected to the greatest mass.
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