Table of contents
- 0. Math Review31m
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- Average Velocity32m
- Intro to Acceleration7m
- Position-Time Graphs & Velocity26m
- Conceptual Problems with Position-Time Graphs22m
- Velocity-Time Graphs & Acceleration5m
- Calculating Displacement from Velocity-Time Graphs15m
- Conceptual Problems with Velocity-Time Graphs10m
- Calculating Change in Velocity from Acceleration-Time Graphs10m
- Graphing Position, Velocity, and Acceleration Graphs11m
- Kinematics Equations37m
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- Adding Vectors Graphically22m
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- Introduction to Dot Product (Scalar Product)12m
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- Magnetic Field Produced by Loops andSolenoids42m
- Toroidal Solenoids aka Toroids12m
- Biot-Savart Law (Calculus)18m
- Ampere's Law (Calculus)17m
- 30. Induction and Inductance3h 38m
- 31. Alternating Current2h 37m
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- Phasors20m
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- Series LRC Circuits11m
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- Power in AC Circuits5m
- 32. Electromagnetic Waves2h 14m
- 33. Geometric Optics2h 57m
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- 35. Special Relativity2h 10m
6. Intro to Forces (Dynamics)
Newton's Third Law & Action-Reaction Pairs
Problem 21
Textbook Question
World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude m/s2. How much horizontal force must a -kg sprinter exert on the starting blocks to produce this acceleration? Which body exerts the force that propels the sprinter: the blocks or the sprinter herself?

1
Step 1: Begin by identifying the relationship between force, mass, and acceleration using Newton's Second Law of Motion, which is expressed as . Here, is the force, is the mass, and is the acceleration.
Step 2: Substitute the given values into the formula. The mass of the sprinter is kg, and the acceleration is m/s2. The equation becomes .
Step 3: Perform the multiplication to calculate the force. This will give the horizontal force exerted by the sprinter on the starting blocks.
Step 4: Address the second part of the question: The force that propels the sprinter forward is exerted by the starting blocks. According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. The sprinter pushes against the blocks, and the blocks push back with an equal and opposite force, propelling the sprinter forward.
Step 5: Conclude by emphasizing the importance of understanding Newton's laws in analyzing motion and forces. The sprinter's ability to accelerate depends on the reaction force provided by the blocks, which is a direct consequence of the sprinter's action force.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Newton's Second Law of Motion
Newton's Second Law states that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = ma). This principle is crucial for understanding how the sprinter's mass and the desired acceleration relate to the force she must exert on the starting blocks.
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Friction and Force Interaction
Friction is the force that opposes the relative motion of two surfaces in contact. In this scenario, the sprinter exerts a force against the blocks, and the friction between her shoes and the blocks allows her to accelerate. The interaction between these forces determines how effectively she can push off the blocks.
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Static Friction & Equilibrium
Action and Reaction Forces
According to Newton's Third Law, for every action, there is an equal and opposite reaction. When the sprinter pushes against the starting blocks, she exerts a force on them, and in response, the blocks exert an equal force back on her. This reaction force is what propels her forward.
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