PHYS1100 Exam #1 Practice – Step-by-Step Physics Guidance

Q20. Three train cars are tied together and pulled along a straight horizontal and frictionless track by a force of 10 N. (Hint: remember the tension force in the rope)

• a. Draw free-body diagrams for each car individually.

• b. Draw a single free body diagram for a system composed of the three train cars.

Background

Topic: Newton's Laws of Motion, Free-Body Diagrams, and Tension

This question tests your understanding of how to analyze forces acting on connected objects, specifically using free-body diagrams and Newton's Second Law. You will need to consider the forces acting on each car and the system as a whole, including the applied force and the tension in the connecting ropes.

Key Terms and Formulas

• Free-Body Diagram (FBD): A diagram showing all the forces acting on an object.

• Newton's Second Law: $F_{\text{net}} = ma$

• Tension: The force transmitted through a rope or string when it is pulled tight by forces acting from opposite ends.

Step-by-Step Guidance

1. For each car, identify all the forces acting on it. For example, the first car (yellow, $m=3\,\text{kg}$) experiences the applied force $F=10\,\text{N}$ to the left and a tension force to the right from the rope connecting it to the second car.

2. Draw a free-body diagram for each car, labeling the forces clearly. For the middle car, consider the tension from both sides (left and right ropes).

3. For the system as a whole (all three cars together), draw a single free-body diagram. The only external horizontal force is the applied force $F=10\,\text{N}$; internal tensions cancel out.

4. Apply Newton's Second Law to the entire system: $F_{\text{net}} = (m_1 + m_2 + m_3)a$.

5. Set up equations for the forces on each individual car if you want to solve for the tension in the ropes, but do not solve for the final values yet.

Try solving on your own before revealing the answer!

Final Answer:

a. Each car's free-body diagram should show the correct forces: the first car has the applied force and tension, the middle car has tension from both sides, and the last car has only tension pulling it forward.

b. The system's free-body diagram shows only the applied force $F=10\,\text{N}$ acting on the combined mass of $10\,\text{kg}$.

By applying $F_{\text{net}} = ma$, you can find the acceleration and then use it to solve for the tension in the ropes if needed.