# Power | Work and energy | Physics | Khan Academy

TLDRThis script explains the concepts of work and power in physics through the analogy of weightlifters and a car example. It highlights that while both weightlifters perform the same amount of work (1,960 joules), the power (rate of work) differs based on the time taken to lift the weights. The script further clarifies the distinction between average power, calculated over a time interval, and instantaneous power, which refers to the power output at a specific moment. The formula for work (force times distance) and its adaptation to find instantaneous power (force times speed) are also discussed.

###### Takeaways

- ποΈ Work in physics is defined as the amount of energy transferred, specifically the energy given to or taken away from something.
- π Both weightlifters are doing the same amount of work, which is measured by the gravitational potential energy transferred to their weights.
- π Gravitational potential energy is calculated using the formula: work done = mass * gravitational acceleration * height (1,960 joules in this case).
- π Power measures the rate at which work is done and is defined as work done divided by the time it took to do that work.
- β±οΈ The weightlifter lifting faster has a higher power output (1,960 joules per second) compared to the slower one (653 joules per second).
- π A joule per second is a watt (W), named after Scottish engineer James Watt, which is a unit of power.
- π The power output of an engine can be found by dividing the work done on a car (kinetic energy) by the time it took to do that work.
- π Average power output is the total work done over a given time interval, while instantaneous power output is the power at a specific moment in time.
- π Instantaneous power can be calculated without calculus by using the formula: force * speed * cosine of the angle (theta) between the force and velocity.
- π οΈ When the force and velocity are in the same direction, the angle is zero, and the instantaneous power simplifies to force times speed.
- π Understanding the concepts of work, power, and energy is crucial for analyzing and comparing the performance of different systems, such as weightlifters or engines.

###### Q & A

### What is the main difference between the two weightlifters described in the script?

-The main difference is the rate at which they lift their weights. Both do the same amount of work, but one does it faster than the other.

### How is work defined in the context of the script?

-Work is defined as the amount of energy transferred, specifically the amount of energy given to something or taken away from something.

### What is the formula for gravitational potential energy mentioned in the script?

-The script does not explicitly state the formula for gravitational potential energy, but it is typically given as mgh, where m is mass, g is the acceleration due to gravity, and h is the height.

### How much work is done by each weightlifter in the script?

-Each weightlifter does 1,960 joules of work.

### What is power in physics, and how is it related to work?

-Power measures the rate at which work is done. It is defined as the work done divided by the time it took to do that work.

### What are the power outputs of the two weightlifters?

-The weightlifter on the right has a power output of 1,960 joules per second, while the weightlifter on the left has a power output of 653 joules per second.

### Who is James Watt, and how is he related to the unit of power?

-James Watt was a Scottish engineer after whom the unit of power, the watt (W), is named. A watt is equivalent to one joule per second.

### How can you find the power output of an engine in the context of the car example?

-You find the power output of an engine by dividing the work done on the car by the time it took to do that work.

### What is the difference between average power and instantaneous power?

-Average power is the total work done divided by the time interval, while instantaneous power is the power output at a particular moment in time.

### How can you calculate instantaneous power without using calculus?

-You can calculate instantaneous power by using the formula for work (force times distance) and dividing by time, which simplifies to force times speed when the force and velocity are in the same direction.

### What is the significance of the angle theta in the power formula?

-Theta is the angle between the force on the object and the velocity of the object. In many cases, when the force and velocity are in the same direction, theta is zero, and the cosine of theta is 1, making the angle irrelevant in the formula.

###### Outlines

##### ποΈββοΈ Work and Power in Weightlifting

This paragraph discusses the concepts of work and power using the example of two weightlifters. It explains that although both lifters do the same amount of work, measured by the gravitational potential energy transferred to their weights, the rate at which they perform the work differs. The paragraph introduces the concept of power, which is the rate of doing work, and defines it as work done divided by the time taken to do the work. It provides a detailed calculation of the power output for both weightlifters, highlighting the difference between average power and instantaneous power. The explanation includes a discussion on how to calculate instantaneous power using the work formula and the concept of force and velocity.

##### π Power Calculation in Motion

This paragraph further explores the concept of power by applying it to a car's motion. It explains how to calculate the power output of an engine by dividing the work done on the car by the time it takes to do the work. The paragraph provides an example of a car accelerating from rest to a certain speed and calculates the engine's power output using the kinetic energy given to the car. It distinguishes between average power output, which is considered over a time interval, and instantaneous power output, which is the power at a specific moment. The paragraph also discusses methods to find instantaneous power without calculus, emphasizing the relationship between force, speed, and the angle between them.

###### Mindmap

###### Keywords

##### π‘Work

##### π‘Energy

##### π‘Gravitational Potential Energy

##### π‘Power

##### π‘Joule

##### π‘Watt

##### π‘Average Power

##### π‘Instantaneous Power

##### π‘Calculus

##### π‘Force

##### π‘Speed

###### Highlights

Work is defined as the amount of energy transferred.

Work equals the amount of energy given to or taken away from something.

Both weightlifters are giving their weights the same amount of gravitational potential energy.

The formula for gravitational potential energy is used to calculate the work done by each weightlifter.

Power measures the rate at which work is done.

Power is defined as the work done divided by the time it took to do that work.

The weightlifter on the right lifts his weight faster, demonstrating a higher power output.

A joule per second is named a watt, after James Watt.

The example of a car's power output is used to illustrate the concept of power.

Average power output is calculated by dividing the total work done by the time interval.

Instantaneous power can be found without calculus by using the work formula and instantaneous speed.

Instantaneous power is the power output at a particular moment in time.

The formula for work is FD cosine theta, which can be adapted to find instantaneous power.

When force and velocity are in the same direction, the instantaneous power simplifies to force times speed.

Power is the rate at which work is done, distinguishing it as a measure of efficiency and performance.

Average power and instantaneous power can be the same if the power output is constant.

###### Transcripts

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