AP Physics 1 - Work-Energy Theorem

Dan Fullerton
17 Jan 201410:46
EducationalLearning
32 Likes 10 Comments

TLDRThe video script discusses the work-energy theorem, explaining how work done on a system changes its energy. It covers various scenarios, including a chef pushing a cart, a pitcher throwing a baseball, and a force-displacement graph analysis. The examples illustrate how work affects kinetic and potential energies, and demonstrate calculations for final velocities and average forces. The content is engaging, providing a clear understanding of the theorem's practical applications.

Takeaways
  • 📜 The work-energy theorem states that work done on a system changes its energy, affecting kinetic or potential energy based on the nature of the work.
  • 🚀 Positive work by an external force increases a system's total energy, while work done by the system decreases its total energy.
  • 🏃‍♂️ For work resulting in a change of motion, kinetic energy is impacted; for work changing an object's height, gravitational potential energy is affected.
  • 🔄 Work done in compressing or stretching a spring affects the system's elastic potential energy.
  • 🔧 Work against friction impacts the internal energy of a system.
  • 👨‍🍳 Example problem: A chef pushes a 10 kg cart 5 meters with a 10 N force on a frictionless surface, resulting in a 3.2 m/s final velocity.
  • 🥎 Second example: A pitcher throws a 143 g baseball at 45 m/s, and the catcher's hand stops it after 6 cm, exerting an average force of 2413 N.
  • 📊 Final example: An object's final speed is determined from a force vs. displacement graph, with the work done equal to the area under the graph and related to the object's kinetic energy.
  • 🌐 The work done is calculated as the sum of the areas of the geometric shapes in the force-displacement graph.
  • 🎯 The final velocity of an object can be found using the work-energy theorem and the area under the force-displacement graph.
  • 📚 For more information on the work-energy theorem, one can visit a physics education website.
  • 🙂 The presentation concludes with a thank you and well-wishes, encouraging further exploration of the topic.
Q & A
  • What is the work-energy theorem?

    -The work-energy theorem states that when a force does work on a system, the work done changes the energy of the system. Positive work done by an external force increases the system's total energy, while work done by the system decreases its total energy.

  • How does the type of energy affected by work depend on the nature of the work being done?

    -The type of energy affected depends on the nature of the work. If the work results in a change of motion of an object, it impacts the kinetic energy. If the work changes the object's height, it affects gravitational potential energy. Compressing or stretching a spring affects elastic potential energy, and work against friction impacts the internal energy of the system.

  • In the example of the chef pushing a pasty cart, what are the given values?

    -The given values are a mass of 10 kilograms for the cart, a displacement of 5 meters, and a constant horizontal force of 10 Newtons acting on the cart.

  • How much work is done by the chef on the pasty cart?

    -The work done by the chef is 50 joules, calculated as the force (10 Newtons) times the displacement (5 meters).

  • What is the final velocity of the pasty cart?

    -The final velocity of the pasty cart is 3.2 meters per second, calculated using the kinetic energy (50 joules) and the mass of the cart (10 kilograms).

  • What are the given values in the example of the pitcher throwing a baseball?

    -The given values are a mass of 143 grams (0.143 kilograms) for the baseball, an initial velocity of 45 meters per second, and a displacement of the catcher's hand of 6 centimeters (0.06 meters).

  • What is the average force exerted on the catcher's hand when stopping the baseball?

    -The average force exerted on the catcher's hand is 2413 Newtons, calculated using the work-energy theorem and the given values.

  • How can the work done be determined from a force versus displacement graph?

    -The work done can be determined as the area under the force versus displacement graph, which is the sum of the areas of each section of the graph (triangles and rectangles).

  • What are the variables given in the final example involving a force versus displacement graph?

    -The variables given are the maximum force (F max), the displacements (r1, r2, r3), the mass of the object (M), and the object's final speed (V).

  • How is the object's final speed calculated using the work-energy theorem and the force versus displacement graph?

    -The object's final speed is calculated using the formula derived from the work-energy theorem, which relates the area under the force versus displacement graph (work done) to the change in kinetic energy of the object (1/2 MV^2).

  • What is the final speed of the object in terms of the given variables?

    -The final speed of the object is given by the square root of (F max/m) times (-negative r1 + r2 + r3), derived from the work-energy theorem and the area under the force versus displacement graph.

  • Where can one find more information on the work-energy theorem?

    -More information on the work-energy theorem can be found at a plus physics com.

Outlines
00:00
📚 Introduction to the Work-Energy Theorem

This paragraph introduces the work-energy theorem, a fundamental principle in physics that describes the relationship between work done by a force and the change in energy of a system. It explains how positive work done on a system increases its total energy, while work done by the system decreases its energy. The type of energy affected depends on the nature of the work, such as kinetic energy, gravitational potential energy, elastic potential energy, or internal energy. The paragraph also presents a problem involving a chef pushing a pasty cart, aiming to calculate the cart's change in kinetic energy and final velocity using the theorem.

05:01
🏐 Calculating Average Force in Ball Catch

The second paragraph discusses the application of the work-energy theorem to a scenario where a pitcher throws a baseball, and the catcher stops it. The goal is to determine the average force exerted on the catcher's hand. By using the theorem, the paragraph outlines the process of equating the change in kinetic energy to the work done, and then solving for the force using the known values of mass, initial velocity, and displacement. The example illustrates how the theorem can be used to analyze forces in sports and everyday situations.

10:05
📊 Interpreting Force-Displacement Graph for Final Speed

This paragraph focuses on using a force-displacement graph to find an object's final speed, given a net force applied horizontally and the object's initial rest state. The explanation involves calculating the area under the graph to determine the work done and then applying the work-energy theorem to find the change in kinetic energy. The paragraph provides a step-by-step approach to solving the problem, including the mathematical rearrangements needed to isolate the final speed variable. It concludes by presenting a formula that relates the object's final speed to the parameters of the force-displacement graph.

Mindmap
Keywords
💡Work-energy theorem
The work-energy theorem is a fundamental principle in physics that states the work done on an object is directly related to its change in energy. In the context of the video, this theorem is used to calculate changes in kinetic energy when a force acts upon an object. For example, when a chef pushes a cart, the work done by the force results in an increase in the cart's kinetic energy, which can be calculated using the theorem.
💡System
In physics, a system refers to a set of objects or a region of space that is being studied, and upon which forces and other physical quantities can act. In the video, the pasty cart, the baseball, and the object on the frictionless surface are all considered systems. The theorem is applied to these systems to analyze the changes in their energies due to work done by external forces.
💡Kinetic energy
Kinetic energy is the energy of motion. An object in motion possesses kinetic energy, which is directly proportional to its mass and the square of its velocity. In the video, the concept of kinetic energy is crucial for understanding how the work done on the cart and the baseball affects their motion.
💡Gravitational potential energy
Gravitational potential energy is the energy an object possesses due to its position in a gravitational field, typically its height above a reference point. In the video, it is mentioned as one of the types of energy that can change when work is done on a system, specifically when the work involves changing the height of an object.
💡Elastic potential energy
Elastic potential energy is the energy stored in an object when it is stretched, compressed, or deformed elastically. This type of energy is related to the object's ability to return to its original shape after the deforming force is removed. The video mentions elastic potential energy as another form of energy that can change when work is done, particularly when the work involves compressing or stretching a spring.
💡Internal energy
Internal energy refers to the total energy contained within a system, which includes the kinetic and potential energies of the molecules or atoms within the system. In the video, it is mentioned that work done against friction would affect the internal energy of a system, as the energy is converted into heat and other forms of microscopic energy.
💡Force
Force is any action that, when unopposed, will cause an object to accelerate or change its motion. In the video, force is a key concept as it is the means by which work is done on a system, leading to changes in the system's energy.
💡Displacement
Displacement refers to the change in position of an object and is a vector quantity that has both magnitude and direction. In the context of the video, displacement is the distance and direction over which a force acts on an object, which is essential for calculating the work done.
💡Velocity
Velocity is a vector quantity that describes the rate of change of an object's position with respect to time, taking into account both speed and direction. In the video, the concept of velocity is used to calculate the final speed of an object after work has been done on it, using the work-energy theorem.
💡Friction
Friction is a force that opposes the relative motion or tendency of such motion of two surfaces in contact. In the video, friction is mentioned as a force that can do work against a system, affecting its internal energy, particularly in the context of stopping or slowing down a moving object.
💡Net force
Net force, also known as the resultant force, is the vector sum of all the individual forces acting on a system. In the video, the net force is used in the context of a force versus displacement graph to determine the total work done on an object and, subsequently, its final speed.
💡Area under the graph
The area under a graph represents the definite integral of the function that describes the curve. In physics, this is often used to calculate work done, as work is analogous to the area under a force versus displacement graph. The video explains how the work done by a net force on an object can be found by determining the area under the force-displacement curve.
Highlights

Work-energy theorem is discussed, which states that work done on a system changes its energy.

Positive work by an external force increases a system's total energy, while work done by the system decreases it.

The type of energy affected depends on the nature of the work, such as kinetic, gravitational potential, elastic potential, or internal energy.

Example problem: A chef pushes a 10 kg cart 5 meters with a 10 N force on a frictionless surface to find the change in kinetic energy and final velocity.

Work done is calculated as force times displacement, resulting in 50 Joules for the given example.

The final velocity of the cart is determined using the kinetic energy formula and is found to be 3.2 m/s.

Another example involves a pitcher throwing a 143 g baseball at 45 m/s, and the catcher's hand stops it after 6 cm displacement.

The average force exerted on the catcher's hand is calculated using the work-energy theorem and the displacement.

The force calculation results in an average force of 2413 N on the catcher's hand.

The final example is about a force vs. displacement graph to determine an object's final speed given various parameters.

The work done is equated to the area under the force-displacement graph, which is the sum of the areas of different sections.

The object's final speed is derived from the work-energy theorem and the calculated area, involving the formula for kinetic energy.

The final speed formula is simplified to express the speed in terms of the given parameters such as Fmax, r1, r2, r3, and M.

For more information on the work-energy theorem, a reference to aplusphysics.com is provided.

The transcript is a comprehensive guide to understanding and applying the work-energy theorem through various practical examples.

The examples demonstrate the theorem's application in calculating kinetic energy, average force, and final speed in different scenarios.

The work-energy theorem is a fundamental concept in physics with wide-ranging applications in problem-solving and understanding energy dynamics.

Transcripts
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