Work as the transfer of energy | Work and energy | Physics | Khan Academy

Summary

The script explains the concept of work done through the formula Fd cos(theta), highlighting its relation to energy transfer. It illustrates positive work with a skateboarder gaining kinetic energy and negative work with the skateboarder losing energy upon crashing. The script further clarifies the principle using gravitational potential energy, showing how lifting bricks results in positive work done. It concludes by emphasizing that work can be determined by the energy an object gains or loses, applicable to all forms of energy.

Takeaways

• 🔍 The formula for work done is Fd*cosine(theta), which represents the energy transferred to an object.
• 🚀 Positive work done (+200 joules) means the force gives energy to an object.
• 🛑 Negative work done (-200 joules) signifies the force takes energy away from an object.
• 🛴 An example is a 50-kilogram skateboarder who gains 2,500 joules of kinetic energy when moved by a force.
• 🏋️‍♂️ The skateboarder's kinetic energy is the measure of the positive work done by the force.
• 💥 When the skateboarder crashes into a stack of bricks, the bricks do negative work by removing energy.
• 🧱 The work done by the bricks is calculated by the energy they took away from the skateboarder.
• 📈 Lifting bricks upwards transfers energy to them in the form of gravitational potential energy.
• 📐 Gravitational potential energy is calculated using the formula mgh, where m is mass, g is acceleration due to gravity, and h is height.
• 🌐 The concept of work done applies to all types of energy, not just kinetic and potential energy.

Q & A

What is the formula used to calculate the amount of work done?

The formula used to calculate the amount of work done is Fd cosine theta.

How does the amount of work done relate to energy transfer?

The amount of work done represents the amount of energy transferred to an object.

What does a positive value of work done indicate?

A positive value of work done indicates that the force gave energy to the object.

How much kinetic energy did the skateboarder gain when moving at 10 meters per second?

The skateboarder gained 2,500 joules of kinetic energy.

What is the relationship between force and work when the skateboarder crashes into a stack of bricks?

The stack of bricks does negative work on the skateboarder because it takes away energy from the skateboarder.

How much work is done by the bricks on the skateboarder when they come to a stop?

The work done by the bricks on the skateboarder is negative 2,500 joules.

What type of energy is gained by the bricks when they are lifted upwards?

The bricks gain gravitational potential energy when they are lifted upwards.

What is the formula to calculate gravitational potential energy?

The formula to calculate gravitational potential energy is mgh.

How much gravitational potential energy did the 500-kilogram bricks gain when lifted four meters?

The bricks gained 19,600 joules of gravitational potential energy.

What does it mean when a force gives energy to an object?

When a force gives energy to an object, it is doing positive work on that object.

Can the concept of work done be applied to all types of energy?

Yes, the concept of work done can be applied to all types of energy, not just gravitational potential energy and kinetic energy.

Outlines

00:00

🔧 Understanding Work Done Through Energy Transfer

This paragraph explains the concept of work done using the formula Fd cos(theta), which represents the energy transferred to an object. It illustrates the idea with the example of a skateboarder gaining kinetic energy from a force that starts their motion, resulting in positive work done. Conversely, when the skateboarder crashes into a stack of bricks, the bricks do negative work by taking away energy. The paragraph also discusses how to find work done by considering the change in energy, such as gravitational potential energy gained by lifting bricks.

Keywords

💡Work Done

Work done is a measure of energy transfer that occurs when a force causes a displacement of an object. In the video, work done is calculated using the formula Fd cosine theta, where F is the force applied, d is the displacement, and theta is the angle between the force and displacement. The video uses the example of a skateboarder to illustrate how work done is related to the energy given to an object. When the skateboarder starts moving, the force does positive work, transferring energy to the skateboarder.

💡Energy Transfer

Energy transfer refers to the movement of energy from one place to another or one form to another. In the context of the video, energy transfer is demonstrated when a force gives energy to the skateboarder, causing motion, or when the stack of bricks takes away energy from the skateboarder, bringing him to a stop. The video emphasizes that work done is equivalent to the energy transferred to or from an object.

💡Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. The video explains that when a force starts a skateboarder moving at 10 meters per second, the force does work on the skateboarder, resulting in a gain of kinetic energy. The skateboarder's kinetic energy is calculated to be 2,500 joules, indicating the amount of work done by the force.

💡Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. In the video, when bricks are lifted upwards, they gain gravitational potential energy. The formula mgh is used to calculate this energy, where m is mass, g is the acceleration due to gravity, and h is the height. The video states that the bricks gained 19,600 joules of gravitational potential energy, which is also the work done on them.

💡Positive Work

Positive work is done on an object when a force causes it to move in the direction of the force, resulting in an increase in the object's energy. The video uses the skateboarder example to illustrate positive work, where the force applied to start the skateboarder moving does positive work, transferring energy and increasing the skateboarder's kinetic energy.

💡Negative Work

Negative work occurs when a force acts in the opposite direction to the motion of an object, causing a decrease in the object's energy. The video explains negative work using the scenario where the skateboarder crashes into a stack of bricks, which stops him. The bricks do negative work on the skateboarder by taking away his kinetic energy.

💡Displacement

Displacement is the change in position of an object. In the context of work done, displacement is the distance over which a force acts on an object. The video mentions that work done can be calculated using the formula Fd cosine theta, where 'd' represents displacement. The example of the skateboarder moving 10 meters per second illustrates the concept of displacement.

💡Force

Force is any interaction that, when unopposed, will change the motion of an object. The video explains that force is necessary to do work on an object, as it is the agent that transfers energy. The force that starts the skateboarder moving and the force that stops the skateboarder are both examples of forces doing work.

💡Cosine Theta

Cosine theta is a mathematical function that describes the component of the force acting in the direction of displacement. In the work done formula Fd cosine theta, cosine theta accounts for the angle between the force and the displacement. The video mentions this formula but also explains that it's not always necessary to calculate work done this way, as energy transfer can be directly observed.

💡Angle of Force

The angle of force is the angle between the direction of the force applied and the direction of motion or displacement. The video discusses how the angle affects the calculation of work done through the cosine theta component in the formula. It is crucial for understanding the efficiency of energy transfer when the force is not aligned with the direction of motion.

💡Energy Conservation

Energy conservation is the principle that energy cannot be created or destroyed, only transformed from one form to another. The video implies this principle by stating that work done on an object is the energy it gains or loses. The skateboarder's kinetic energy and the bricks' gravitational potential energy are examples of energy transformations.

Highlights

Work done can be calculated using the formula Fd cosine theta.

Work done represents the energy transferred to an object.

Positive work done indicates energy given to an object.

Negative work done indicates energy taken away from an object.

Determining energy gain or loss can provide an alternate way to find work done.

Example of a skateboarder gaining kinetic energy from a force.

The skateboarder's kinetic energy gain is 2,500 joules.

Work done by the force on the skateboarder is positive 2,500 joules.

Force doing positive work gives energy to an object.

Force doing negative work takes away energy from an object.

Example of a skateboarder losing kinetic energy upon crashing into bricks.

The bricks do negative work by taking away the skateboarder's energy.

Work done by the bricks is negative 2,500 joules.

Lifting bricks upwards gives them gravitational potential energy.

Gravitational potential energy is calculated using the formula mgh.

The bricks gain 19,600 joules of gravitational potential energy.

Work done on the bricks is positive 19,600 joules.

The concept of work done applies to all types of energy.

Work done by a force can always be found by determining the energy given or taken away.

Transcripts

One way to find the amount of work done

is by using the formula Fd cosine theta.

But this number for the amount of work done

represents the amount of energy transferred to an object.

For instance, if you solve for the work done

and you get positive 200 joules, it

means that the force gave something 200 joules of energy.

So if you have a way of determining

the amount of energy that something gains or loses,

then you have an alternate way of finding the work done,

since the work done on an object is the amount of energy

it gains or loses.

For instance, imagine a 50-kilogram skateboarder

that starts at rest.

If a force starts the skateboarder moving

at 10 meters per second, that force

did work on the skateboarder since it gave the skateboarder

energy.

The amount of kinetic energy gained by the skateboarder

is 2,500 joules.

That means that the work done by the force on the skateboarder

was positive 2,500 joules.

It's positive because the force on the skateboarder

gave the skateboarder 2,500 joules.

If a force gives energy to an object,

then the force is doing positive work on that object.

And if a force takes away energy from an object,

the force is doing negative work on that object.

Now imagine that the skateboarder, who's

moving with 10 meters per second,

gets stopped because he crashes into a stack of bricks.

The stack of bricks does negative work

on the skateboarder because it takes away energy

from the skateboarder.

To find the work done by the stack of bricks,

we just need to figure out how much energy it took away

from the skateboarder.

Since the skateboarder started with 2,500 joules

of kinetic energy and ends with zero joules of kinetic energy,

it means that the work done by the bricks on the skateboarder

was negative 2,500 joules.

It's negative because the bricks took away energy

from the skateboarder.

Let's say we instead lift the bricks, which

are 500 kilograms, upwards a distance of four meters.

To find the work that we've done on the bricks,

we could use Fd cosine theta.

But we don't have to.

We could just figure out the amount of energy

that we've given to the bricks.

The bricks gain energy here.

And they're gaining gravitational potential energy,

which is given by the formula mgh.

If we solve, we get that the bricks

gained 19,600 joules of gravitational potential energy.

That means that the work we did on the bricks

was positive 19,600 joules.

It's positive because our force gave the bricks energy.

This idea doesn't just work with gravitational potential energy

and kinetic energy.

It works for every kind of energy.

You can always find the work done by a force on an object

if you could determine the energy that that force gives

or takes away from that object.

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