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Ch 05: Force and Motion
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 05: Force and MotionProblem 44
Chapter 5, Problem 44

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.

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Step 1: Understand the problem. The rocket is being launched straight up, and air resistance is not negligible. This means there are multiple forces acting on the rocket, including gravity, thrust, and air resistance. We need to create three diagrams: a motion diagram, a force-identification diagram, and a free-body diagram.
Step 2: Draw the motion diagram. A motion diagram represents the position and velocity of the rocket at different points in time. Since the rocket is accelerating upward due to thrust, the velocity vectors should increase in length as the rocket moves upward. However, as air resistance increases, the rate of acceleration will decrease over time.
Step 3: Create the force-identification diagram. Identify all the forces acting on the rocket. These include: (1) the gravitational force (\( F_g = m \cdot g \)), which acts downward, (2) the thrust force (\( F_{thrust} \)), which acts upward, and (3) the air resistance force (\( F_{air} \)), which acts downward and opposes the motion of the rocket.
Step 4: Draw the free-body diagram. Represent the rocket as a dot or a small box. Draw vectors to represent the forces acting on the rocket. The upward vector represents the thrust force (\( F_{thrust} \)), and the two downward vectors represent the gravitational force (\( F_g \)) and the air resistance force (\( F_{air} \)). Ensure the lengths of the vectors are proportional to the magnitudes of the forces.
Step 5: Analyze the net force. The net force (\( F_{net} \)) acting on the rocket is the sum of all forces: \( F_{net} = F_{thrust} - F_g - F_{air} \). This net force determines the rocket's acceleration according to Newton's second law: \( F_{net} = m \cdot a \). Use this relationship to further analyze the motion if needed.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Motion Diagrams

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

Force identification involves recognizing and categorizing the different forces acting on an object in a given scenario. In the case of the rocket launch, it is essential to identify the thrust, gravitational force, and air resistance to understand how they interact and affect the rocket's ascent. This analysis is fundamental for applying Newton's laws of motion.
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Related Practice
Textbook Question

A rubber ball bounces. We'd like to understand how the ball bounces. Draw a free-body diagram of the ball during its contact with the ground. Is there a net force acting on the ball? If so, in which direction?

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Textbook Question

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 model rocket is fired straight down from the top of a tower.

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Textbook Question

A rubber ball bounces. We'd like to understand how the ball bounces. A rubber ball has been dropped and is bouncing off the floor. Draw a motion diagram of the ball during the brief time interval that it is in contact with the floor. Show 4 or 5 frames as the ball compresses, then another 4 or 5 frames as it expands. What is the direction of a during each of these parts of the motion?

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Textbook Question

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if The force is halved and the object's mass is doubled?

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Textbook Question

Problems 35, 36, 37, 38, 39, and 40 show a free-body diagram. For each: Identify the direction of the acceleration vector a and show it as a vector next to your diagram. Or, if appropriate, write a = 0.

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Textbook Question

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 Styrofoam ball has just been shot straight up. Air resistance is not negligible.

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