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# Introduction to work and energy

Introduction to work and energy. Created by Sal Khan.

## Want to join the conversation?

• I don't quite understand the difference between negative work and no work? •  Negative work can be understood this way:
Car breaks down while going uphill and it starts to roll downward. You, as a good samaritan, try to stop the car from rolling down the slope by pushing on it with all your might. The force you apply on the car is directed uphill but alas, it's not enough to stop the car. The car continues to move downhill, that is, it's displacement is in a direction opposite to the force you are applying. This means you are doing negative work on the car. If you draw the free body diagram for this car, rolling down the incline, you'll see that the component of gravity parallel to the incline is doing the positive work because both this component and the displacement are in the same direction.

Now suppose, more bystanders come along to help stop the car. Everyone pushes on the car uphill so that the car slows down and eventually stops. This happened because the negative work that each person was doing eventually became big enough to cancel out the work that gravity was doing. Once the car stops and the people continue to push it uphill, the car will start rolling upward, in the direction of the applied force and now you'll get positive work.
During this scenario, note that the normal force on the car from the incline is perpendicular to the surface and the car and it does zero work because there is no motion along its direction.
I hope this helps to assuage your doubts.
• Sal says that work = force . distance... how can a vector be multiplied with a scalar to yield a scalar? • The actual formula for work is

W = F · s,
i.e. Work is the scalar product of the vectors Force and displacement, not necessarily distance.

Scalar product is so called because it returns a scalar, which in this case is Work. (It is also called "dot product" because of the "·" symbol between the vectors in the formula.) So in fact, Work does not equal Force times distance; Mr. Khan did a white lie there.

Why do I say he did a white lie? Well, in the case of moving in a straight line (with force in same direction as displacement),

the scalar product has the same effect as multiplying the magnitudes of the 2 vectors, and the magnitude of displacement vector is equal to distance:
||s||=d
so W=F · s=||F||*||s||=F*d.

So in this case, Mr. Khan's definition of Work is correct. But this obviously won't work for other cases (e.g. NOT moving in a straight line); Mr. Khan gave this definition for introduction's sake.
• the law said that the energy can neither be created nor be destroyed if its true and we need energy to move our body then where did the energy went for example before moving our hand the energy was stored there but after moving it the energy is used the question is where is the used energy after moving the hand ? • So the energy associated with moving out hands is dissipated in several ways. One way is release as thermal energy within our actual body - so when we use our muscles, they actually heat up, because our bodies have to do a lot of exothermic (heat releasing) chemical reactions to actually create muscle contraction. We also interact with air molecules, kind of "swatting" them, which will vaguely increase their speed.

When we do small motions, like waving our hand once or twice at a friend, this isn't going to release a noticeable amount of heat... but if you run a marathon, I guarantee your legs will feel warm, and your body will heat up at the massive amount of work your body does over the course of the marathon!

Hope this helps.
• what is the difference between work,energy and power？ • if i hold a dumbell with my hand i exert a force on the dumbell to keep it suspended in the air, now if i dont move at all i.e displacement of 0 then we say that the work done is 0J. However if i hold the ball for a long period of time i do feel tired so there is a energy transfer happening , so how does that work (no pun intended)?? • You feel tired because the muscles of your arm are continuously contracting and relaxing and thereby using chemical energy of your body. But it's not the kind of work as we define in physics because the dumbbell stays put. You are not moving it through any distance. But holding it in place is making your body expend energy in the form of heat and local cellular work.
• I don't understand; it takes the same amount of energy to accelerate an object and let it travel 1 m as to accelerate it the same amount and let it travel 10 m (in space, because of inertia.) According to the formula for work, these ore different amounts of work, but the same energy is needed. • Work is force*distance. In space, the result of doing work will be that the object has velocity (and kinetic energy. More work will give it more velocity. Once the object has reached constant velocity, that means the force is no longer being applied (it is moving just by inertia). No more work is done at that point. The object will continue to go indefinitely but no work is being done anymore once it is no longer experiencing force.
• Hi!

If I am carrying a book in my hand ( till chest ) and then walk till 10 m then is it called work done? or not,
as 2 forces are acting to each other
- gravitational
- my hand's force to keep it upright
(1 vote) • Why is Work(W) the same as Kinetic Energy(KE) when F*d is converted into 1/2mv^2, can Work not be used/ is Work not used to describe every kind of Energy/Energy transfer? Could Work not just as easily be used to describe the transfer of heat or electricity to an object rather than applying a physical force? This video gives me the impression that Work is solely linked to kinetic energy and physical movement. • At , He says work is energy transferred by force, Using this definition shouldn't the formula be Work = Energy times Force ? • What is difference between work and energy ?? 