# Work and Energy

TLDRIn this AP Physics essentials video, Mr. Andersen explores the relationship between work and energy through the sport of pole vaulting and provides a detailed explanation of how kinetic and potential energy transform during the process. He illustrates the concept with a practical example of a bus being pushed with a constant force, calculating the work done and the resulting kinetic energy. The video also covers the application of trigonometry for forces at an angle and emphasizes the importance of understanding work-energy principles for predicting changes in mechanical energy.

###### Takeaways

- ๐ The world record in women's pole vault is held by Elena Isinbekova, with a record height of 16 feet 7 inches.
- ๐ In pole vaulting, athletes convert kinetic energy from their run into elastic potential energy in the pole, and then into gravitational potential energy over the bar.
- ๐โโ๏ธ The concept of work in physics is central to understanding how force and displacement contribute to the energy transfer during physical activities like pole vaulting.
- ๐ Work done can be visualized and calculated using a force-displacement graph, where the area under the curve represents the amount of work.
- ๐ An example of calculating work involves applying a 12,000 N force to move a bus 48 meters, resulting in 580,000 joules of work done and an increase in kinetic energy.
- ๐ The work-energy theorem allows us to determine changes in mechanical energy and, given enough information, calculate final velocities based on work done.
- ๐ข When dealing with forces at an angle, trigonometry is used to find the component of the force parallel to the displacement to accurately calculate work.
- ๐ The area under a force-displacement graph represents the total work done on an object and the energy transferred to the system.
- ๐ข In the given example, a 3 kg block experiences work done by varying forces, which can be calculated by determining the area under the curve for each segment of the graph.
- ๐ The conservation of energy principle is key in understanding that the work done on a system is equivalent to the change in mechanical energy, assuming no energy is lost to friction or other resistive forces.
- ๐ค The script encourages viewers to apply these concepts to make predictions about changes in mechanical energy and to solve practical problems involving work and energy.

###### Q & A

### What is the main topic of the video?

-The main topic of the video is work and energy, specifically in the context of physics and how it relates to the pole vault event.

### Who holds the world record in women's pole vault, and what is her record height?

-Elena Isinbeava holds the world record in women's pole vault with a height of sixteen feet seven inches.

### How does the pole vaulter increase their kinetic energy during the run-up?

-The pole vaulter increases their kinetic energy by running down the runway, which involves gaining speed and momentum.

### What type of energy is stored in the pole during the pole vault?

-During the pole vault, the kinetic energy of the runner is stored as elastic potential energy in the pole.

### What is the relationship between the energy stored on the runway and the potential energy at the top in a pole vault?

-The amount of energy stored on the runway is equivalent to the amount of gravitational potential energy the vaulter has at the top of the jump.

### What is the significance of displacement in the context of work done in physics?

-Displacement is significant because it is the distance over which a force is applied, and it is necessary for work to be done. Work is defined as the force applied over a displacement.

### How can a force versus displacement graph be used to calculate work done?

-A force versus displacement graph can be used to calculate work done by finding the area under the curve of the graph, which represents the mechanical energy added to the system.

### What is the formula for calculating work done on an object?

-The formula for calculating work done on an object is W = F * s, where W is work, F is the force applied, and s is the displacement of the object.

### How can the work done on the bus in the example be converted into kinetic energy?

-The work done on the bus (580,000 joules) is converted into kinetic energy, which increases the bus's velocity from 0 to 13 meters per second, assuming no energy is lost to friction.

### How can the angle of the force relative to the displacement affect the amount of work done?

-The angle of the force relative to the displacement affects the amount of work done because only the component of the force parallel to the displacement does work. This can be calculated using trigonometry, such as finding the cosine of the angle.

### What is the importance of understanding the work-energy theorem?

-Understanding the work-energy theorem is important because it allows us to predict changes in mechanical energy within a system and to calculate quantities such as velocity, given the work done and the conservation of energy.

###### Outlines

##### ๐ Understanding Work and Energy through Pole Vaulting

This paragraph introduces the concept of work and energy using the example of pole vaulting, specifically highlighting the world record set by Elena Isinbeava. It explains how the kinetic energy gained by the vaulter during the run-up is converted into gravitational potential energy, and then back into kinetic energy. The paragraph also discusses the mechanical work done by the pole, the importance of displacement caused by an unbalanced force, and how work can be calculated using a force-displacement graph. A practical problem involving a bus being pushed with a constant force is used to illustrate the calculation of work and its equivalence to kinetic energy, leading to the determination of the bus's final velocity using the work-energy theorem.

##### ๐ Calculating Work with Varying Forces and Displacements

This paragraph delves into the calculation of work when forces vary over time or distance. It uses the analogy of a block being pushed with a constant force for a certain distance, followed by a reduction in force. The concept of calculating work through the area under a force-displacement graph is emphasized, with a step-by-step explanation of how to determine the work done in each segment of the graph. The paragraph concludes with a review of the principles of mechanical energy conservation and the application of the work-energy theorem to predict changes in energy and velocity, reinforcing the concepts learned through the examples provided.

###### Mindmap

###### Keywords

##### ๐กWork

##### ๐กEnergy

##### ๐กKinetic Energy

##### ๐กPotential Energy

##### ๐กMechanical Energy

##### ๐กForce

##### ๐กDisplacement

##### ๐กConservation of Energy

##### ๐กVelocity

##### ๐กParallel Force

##### ๐กForce-Displacement Graph

###### Highlights

The topic of the video is work and energy, with a focus on the pole vault as an example of the relationship between energy and work.

Elena Isinbeava holds the world record in women's pole vault at sixteen feet seven inches.

The physics of pole vaulting involves converting kinetic energy into elastic potential energy and then into gravitational potential energy.

The pole does work by applying a force over a distance, which is a key concept in understanding mechanical energy.

In a system, mechanical energy can be added or removed, and it can be in the form of potential or kinetic energy.

Displacement in a system is caused by an unequal parallel force, which is essential for work to be done.

Work can be calculated using a force versus displacement graph, where the area under the curve represents the amount of work done.

A constant force applied over a displacement results in work equal to the product of the force and the displacement.

An example problem involves calculating the work done on a bus with a 12,000 newton force over a 48-meter displacement, resulting in 580,000 joules of work.

The work done on an object is equivalent to the change in its kinetic energy.

Using the work-energy theorem, one can determine the final velocity of an object given the work done on it.

A bus with a mass of 6,500 kilograms reaches a velocity of 13 meters per second after work is done on it.

In a different scenario, a giant pulls a bus with a 12,000 newton force at a 38-degree angle, requiring trigonometry to calculate the work done.

The force versus displacement graph is a useful tool for visualizing and calculating work done on an object.

An example with a 3-kilogram block demonstrates how to calculate work done by analyzing the area under a force-displacement graph.

The total work done on the block is the sum of the work calculated from the areas of rectangles and triangles under the force-displacement graph.

The concept of work-energy theorem allows for predictions about changes in mechanical energy and the conservation of energy in a system.

The video aims to help viewers understand how to apply these concepts to real-world problems, such as determining the velocity of a bus.

###### Transcripts

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