Problems 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, and 52 describe a situation. For each, draw a motion diagram, a force-identification diagram, and a free-body diagram. A rocket is being launched straight up. Air resistance is not negligible.

Verified step by step guidance

1. Identify the object of interest and the forces acting on it. In this case, the object is the rocket. The forces acting on the rocket include the gravitational force pulling it downwards, the thrust force from the rocket engines pushing it upwards, and the air resistance acting downwards opposing the motion.
2. Draw the motion diagram. This diagram should show the rocket's position at several time intervals. Since the rocket is moving upwards, the positions should be spaced further apart at the beginning (if assuming constant acceleration) and may get closer as air resistance increases.
3. Create the force-identification diagram. This diagram labels all the forces acting on the rocket without considering their magnitudes. Label the downward gravitational force (weight), the upward thrust from the engines, and the downward air resistance.
4. Sketch the free-body diagram. This diagram isolates the rocket and represents each force acting on it with a vector arrow. The length of each arrow should be proportional to the magnitude of the forces. The weight (mg) is directed downwards, the thrust is directed upwards, and the air resistance is also directed downwards.
5. Analyze the forces to set up the equations of motion. Use Newton's second law, F = ma, where F is the net force (thrust minus weight minus air resistance), m is the mass of the rocket, and a is the acceleration. This equation will help in understanding how the forces balance or unbalance to cause acceleration.

Key Concepts

Motion Diagrams

A motion diagram visually represents the position of an object at various time intervals, illustrating its trajectory and velocity. In the context of a rocket launch, it helps to depict the rocket's upward motion and any changes in speed due to forces acting on it, such as thrust and air resistance.

Free-Body Diagrams

A free-body diagram is a graphical representation that shows all the forces acting on an object. For the rocket, this includes the thrust force from the engines, the gravitational force pulling it downward, and the air resistance opposing its motion. Understanding these forces is crucial for analyzing the rocket's acceleration and overall motion.

Force Identification

Force identification involves recognizing and categorizing the various forces acting on an object in a given scenario. In the case of the rocket launch, it is essential to identify the thrust, weight, and drag forces to understand how they interact and affect the rocket's ascent, especially since air resistance is significant.