Introduction to Power

Flipping Physics

18 May 201605:52

EducationalLearning

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TLDRIn this educational dialogue, the participants explore the concepts of work and power in physics. Despite two different scenarios involving books being lifted, the work done by the force applied is the same due to equal displacement and force direction. However, the rate of work, or power, differs because of the varying time taken and velocity of the book's movement. The discussion clarifies the relationship between work (force times displacement times cosine theta), power (work over time or force times velocity times cosine theta), and their respective units (joules and watts). The origin of the term 'watt' is also touched upon, linking it to James Watt and the historical comparison of steam engines to horse power.

Takeaways

🔧 The work done by the force applied is the same in both examples despite differences in time taken.
⏱️ Time is a factor that affects power but not work; power is the rate at which work is done.
📝 The equation for work is force times displacement times cosine of the angle (θ).
📈 Both books have the same displacement and the force and displacement are collinear, resulting in the same work done.
🚀 The book on the left moves faster, but both books have constant velocity, meaning their acceleration is zero.
🔄 The net force in both cases is the applied force minus the force of gravity, resulting in equal forces since the mass of the books is the same.
⚡ Power, derived from work over time, is greater for the book on the left due to its shorter time duration.
🌟 Power can also be expressed as force times velocity times cosine of the angle (θ), similar to the work equation.
📏 Work and power are scalar quantities, while power is also represented in units like watts and horsepower.
🐎 The unit of horsepower (746 watts) originates from James Watt's comparison of steam engines to the work of horses in the late 1700s.

Q & A

What is the main difference between the two examples discussed in the transcript?
-The main difference is the time taken for the work to be done, even though the amount of work done by the force applied is the same in both examples.
How is power related to work and time?
-Power is the rate at which work is done, calculated as work divided by the change in time. The units for power are joules per second, also known as watts.
What is the equation for work in the context of the transcript?
-Work is calculated as the force times displacement times cosine of the angle (theta).
Why does the force applied have to be considered when calculating power?
-Power is always done by a particular force or the net force, so identifying the force delivering the power is essential for accurate power calculation.
What is the significance of the angle (theta) in the power equation?
-The angle in cosine theta must be the angle between the direction of the force and the direction of the velocity, affecting the calculation of power based on the force's effective component in the direction of motion.
How does the concept of acceleration relate to the examples in the transcript?
-Although the books move at different velocities, they both move at a constant velocity, meaning their acceleration in the y-direction is zero, and thus the force applied equals the force of gravity in both cases.
What is the relationship between velocity and displacement over change in time?
-Displacement over change in time is equal to velocity, highlighting the connection between these two quantities in the context of motion and work.
Why are work and power considered scalar quantities?
-Work and power are scalar quantities because they do not involve direction, only magnitude, making them easier to calculate and compare without considering orientation in space.
What is the historical origin of the unit 'horsepower'?
-Horsepower is a unit of measurement for power that dates back to the late 1700s when James Watt needed a way to compare the efficiency of steam engines to the power of horses. It is derived from his measurements of horses pulling a mill, equating to 746 watts.
How is the symbol for watts used in the transcript?
-The symbol for watts is a capital 'W', but in the transcript, it is mentioned that the full word 'watts' is always written out to avoid confusion with 'work', except in cases where a prefix is used, such as kilowatts or milliwatts.
What can be inferred about the book's motion in the examples?
-In both examples, the books are moving at a constant velocity, indicated by the absence of acceleration in the y-direction, which is zero due to the balance of forces (applied force equals gravitational force).

Outlines

00:00

📚 Understanding Work and Power in Physics

This paragraph delves into the concepts of work and power in physics, using a dialogue format to explore these ideas. The discussion begins with an example of two scenarios where the work done by a force is the same, despite differences in time taken and motion. The conversation clarifies that work is calculated as force times displacement times the cosine of the angle between the force and displacement. It then transitions to power, defined as work done over a change in time, and introduces the equation for power, which is similar to the work equation but includes velocity. The paragraph emphasizes the scalar nature of work and power and introduces the unit of power, the watt, with a brief historical context of its origin from James Watt's comparison of steam engines to horse power.

05:04

🏇 The Origin of Horsepower and Watt as a Unit

This paragraph continues the discussion on power by exploring the historical origin of the unit 'horsepower'. It explains that the concept dates back to the late 1700s when James Watt, a Scottish inventor, needed a way to compare the output of his steam engines to the work done by horses. Through his measurements of horses pulling a mill, he established that 746 watts is equivalent to one horsepower. The conversation concludes with a reflection on the somewhat arbitrary nature of equating a horse's power to 746 watts.

Mindmap

Keywords

💡Work

Work in the context of physics is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. In the video, it is emphasized that even though the two examples involve different timescales, the work done by the force applied is the same because both books are displaced the same amount and the force and displacement are in the same direction, making the cosine of the angle zero degrees.

💡Power

Power is the rate at which work is done or energy is transferred. It is a measure of how quickly work is performed and is calculated as work divided by the change in time. In the video, it is explained that even though the work done is the same in both examples, the power delivered by the force applied is different because the time taken for each example varies, leading to a different rate of energy transfer.

💡Force

In physics, force is any action that, when unopposed, will cause a body to accelerate or change its direction of motion. In the video, force is applied to books in both examples to lift them upward, and it is explained that the force applied is equal to the force of gravity because the books are moving at a constant velocity, indicating that the net force (and thus the applied force) is balanced by gravity.

💡Displacement

Displacement refers to the change in position of an object. It is a vector quantity that considers both the distance and the direction from the initial to the final position. In the video, displacement is crucial for calculating work, as it is the distance the object moves in the direction of the applied force.

💡Angle (theta)

The angle, often denoted by the Greek letter theta (θ), is the measure of the angle between two vectors. In the context of the video, it is the angle between the direction of the force and the direction of the displacement or velocity. The cosine of this angle is used in the equations for work and power to determine the component of the force or velocity that is doing work or delivering power.

💡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, velocity is important when discussing power because it is a factor in the equation for power, which relates the rate of doing work to the velocity of the object.

💡Acceleration

Acceleration is the rate of change of velocity of an object with respect to time and is a vector quantity that describes how quickly an object speeds up, slows down, or changes direction. In the video, it is clarified that despite one book moving faster than the other, both books have zero acceleration in the y-direction because they are moving at a constant velocity.

💡Cosine

The cosine is a mathematical function that relates the angle of a right triangle to the ratio of the length of its adjacent side to the length of its hypotenuse. In the context of the video, cosine is used in the equations for work and power to determine the component of the force or velocity that is in the direction of the displacement or movement, which is crucial for calculating the work done or power delivered.

💡Joules and Watts

Joules and watts are units of measurement used in physics. A joule is a unit of energy, work, or amount of heat, and it represents the work done when a force of one newton displaces an object by one meter in the direction of the force. A watt is a unit of power, which is the rate of doing work or the rate of energy transfer, and it is equal to one joule per second.

💡Horsepower

Horsepower is a unit of power that originated as a measurement of the output of steam engines compared to the work done by horses. It is defined as the power required to raise a weight of 550 pounds by one foot in one second, which is approximately equal to 746 watts.

💡Milliwatts

A milliwatt is a unit of power equal to one-thousandth of a watt (0.001 W). It is used to express very small amounts of power, often in the context of electronic devices or low-power applications.

Highlights

The work done by the force applied is the same in two different examples despite taking different amounts of time.

Power is related to the change in time, defined as work over change in time.

The equation for work is force times displacement times cosine theta.

Both books displaced the same amount, and the force and displacement are in the same direction, resulting in the same work done.

Acceleration and velocity are different; both books move at a constant velocity, hence their acceleration in the y-direction is zero.

The force applied equals the force of gravity because the books are in constant velocity, indicating the same force applied in both cases.

The example with the book moving faster delivers more power due to the shorter time taken.

Power can also be expressed as force times velocity times cosine theta, highlighting its relationship with work.

The unit of power is watts, which is joules per second.

The symbol for watts is a capital W, but it is often written out fully to avoid confusion with 'work'.

Displacement over change in time equals velocity, connecting the concepts of power and velocity.

When calculating power, it's crucial to identify which force is delivering the power and consider the angle between the force and velocity directions.

Power is a scalar quantity, as both work and change in time are scalars.

Horsepower is a common dimension for power, with one horsepower equaling 746 watts.

The concept of horsepower dates back to the late 1700s when James Watt compared steam engines to the work of horses.

The conversation format used in the transcript effectively illustrates the principles of work and power in physics.

The transcript provides a clear and engaging explanation of the relationship between work, power, and time.

Transcripts

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Introduction to Power

Takeaways

Q & A

What is the main difference between the two examples discussed in the transcript?

How is power related to work and time?

What is the equation for work in the context of the transcript?

Why does the force applied have to be considered when calculating power?

What is the significance of the angle (theta) in the power equation?

How does the concept of acceleration relate to the examples in the transcript?

What is the relationship between velocity and displacement over change in time?

Why are work and power considered scalar quantities?

What is the historical origin of the unit 'horsepower'?

How is the symbol for watts used in the transcript?

What can be inferred about the book's motion in the examples?