Textbook Question
A tennis racket swung over the server's head hits a tennis ball horizontally. Draw a free-body diagram for each object in the system. Use dashed lines to connect members of an action/reaction pair.
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6. Intro to Forces (Dynamics)
Types Of Forces & Free Body Diagrams
Problem 31a
Textbook Question
(I) Sketch the free-body diagram of a baseball at the moment it is hit by the bat.
Verified step by step guidance1
Step 1: Understand the scenario. A free-body diagram is a visual representation of all the forces acting on an object. In this case, the object is a baseball, and we need to analyze the forces acting on it at the moment it is hit by the bat.
Step 2: Identify the forces acting on the baseball. At the moment the bat hits the baseball, the following forces are present: (1) The force exerted by the bat on the baseball (a contact force), (2) The gravitational force acting downward due to the weight of the baseball, and (3) Air resistance, which may act opposite to the direction of motion if the baseball is already moving.
Step 3: Draw the free-body diagram for the baseball. Represent the baseball as a dot or small circle. Use arrows to indicate the forces: (1) Draw an arrow pointing in the direction of the bat's force (this is typically horizontal or at an angle, depending on the hit), (2) Draw a downward arrow to represent the gravitational force (labeled as \( F_g = m \cdot g \)), and (3) If air resistance is significant, draw an arrow opposite to the motion of the baseball to represent it.
Step 4: Label the forces clearly. For example, label the force from the bat as \( F_{bat} \), the gravitational force as \( F_g \), and the air resistance as \( F_{air} \). Ensure the lengths of the arrows are proportional to the relative magnitudes of the forces, if known.
Step 5: Repeat the process for the second scenario (if applicable). If the problem asks for a free-body diagram at a different moment (e.g., after the baseball is no longer in contact with the bat), update the diagram to reflect the forces acting at that time. For instance, after the hit, the force from the bat would no longer be present, leaving only gravitational force and air resistance.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Free-Body Diagram
A free-body diagram is a graphical representation used to visualize the forces acting on an object. It typically includes the object in question, represented as a dot or a simple shape, and arrows indicating the direction and magnitude of each force. This tool helps in analyzing the net force and understanding the motion of the object based on Newton's laws.
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Forces Acting on the Baseball
When a baseball is hit by a bat, several forces act on it, including the force exerted by the bat, gravitational force pulling it downward, and air resistance opposing its motion. The force from the bat is typically much greater than the other forces at the moment of impact, resulting in a rapid acceleration of the baseball. Understanding these forces is crucial for accurately sketching the free-body diagram.
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Newton's Second Law of Motion
Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, expressed mathematically as F=ma. This principle is essential for understanding how the baseball will move after being hit, as the net force from the bat will cause it to accelerate in the direction of the applied force, while gravity and air resistance will also influence its trajectory.
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