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## High school physics

### Course: High school physics>Unit 5

Lesson 3: Work-energy theorem

# Work and the work-energy principle

Physicists define work as the amount of energy transferred by a force. Learn about the formula for calculating work, and how this relates to the work-energy principle, which states that the net work done on an object is equal to the change in its kinetic energy. Created by David SantoPietro.

## Want to join the conversation?

• Why does one need a cos and theta when we can easily get the work by multiplying F and displacement ?
- thoroughly confused •  Imagine that your F is at and angle starting at the origin and pointing somewhere between the x and y axis and you distance is along the x axis. To calculate the word done we need to take the x component of the our F and multiply it by the distance. And easy way to do this is multiplying the cosine of the angle and the F. And only the x component of our force matter because the y component is going vertical and doesn't do anything to with the x-axis movement. If that doesn't make sense imagine F is the hypotenuse of your triangle. And the x-component is the base and the y-component is the height. Knowing the angle between the x-axis and our hypotenuse (F) and using our handy knowledge of trigonometry, we know we can use the cosine of our angle multiplied by our hypotenuse (F) to find the x-component because of the intrinsic ration in triangles. I hope this helps.
• Hi, i'm unclear about why Wnet=0 indicates that an object is maintained at constant. Could someone please kindly help to explain the relationship for this?

The reason for having this doubt:
If Wnet=0, doesn't it mean that the object is not moving at all? Since Wnet also = Fnet(d), it could mean that d=0. Hence there is no work done.

If looking at the application of the work energy theorem whereby acceleration is assumed to be constant & Wnet=1/2(m)(vnet^2) with Wnet=0, it would mean that the net velocity = 0 as the mass of an object will not change. Hence, isn't it that the object will not be moving, instead of moving at a constant velocity?

Please kindly help out in clarifying my understanding. Thank you. • .. the condition is that if the object is moving at a constant speed/velocity then the net work will be zero is TRUE. this is bcoz when u move at a constant velocity then the acceleration is zero bcoz u maintain ur speed instead of increasing or decreasing ur speed . it leads to zero acceleration and NOT constant acceleration. force is mass times acceleration. since u have a zero acceleration your force is going to be zero . and since work is force times displacement ur work will also be zero.

the possibility raised by u that d = 0 is true and work will also be 0.

if the acceleration is constant it means that ur velocity keeps increasing by equal amounts in equal intervals of time.... hence it cannot be zero. i hope that clarifies......if u still have any doubt plz ask.
• Hi,
Just trying to understand Kinetic energy. If a mass travels at a constant velocity in one direction and then moves in the opposite direction at the same velocity will the kinetic energy remain the same? • Wow thats a great question....

How to figure out the answer?

First thing that comes to mind is that energy is not a vector. This means that, whatever the direction, it will have the same value.

Even though velocity is part of the equation for KE; because it is squared... it loses its vector qualities.
• Gravitational Potential Energy does negative work right?
So why isn't it taking away energy from an object which goes up to a certain height? As told in the previous lecture, the object possesses Potential energy. I dont understand ... why does it have energy at all?! • To calculate Grav. potential energy we use Ep = -G (m1m2/r).
In order to have 0 grav. potential energy, the denominator, r, would need to be really massive, so that you were "out of the grav, field." But Newton says that grav, fields extend throughout the universe (even though I am hundreds thousands if not millions of miles away from Pluto its mass and my mass are interacting via our respective grav fields.) So it stands to reason that if you are moving something away from an object, you are moving it towards infinity, so towards 0 grav. potential. But if you let go, it converts the energy you supplied it to kinetic energy, so the conservation of energy says that it must have less energy then it did before you let go. In order for it to have less energy than 0, it must be negative.

It has energy at all because it is still in the gravitational field of the larger object.
Hope this helps!
• What is the exact meaning of 'NET' Force and 'NET' Work? • I don't understand 2 things: 1) What are the conditions for when this formula is valid? 2) How does potential energy relate? What if an object is lifted straight up onto a table and placed there? The energy of the system has changed, even if the starting and ending kinetic energies are the same.

I'd learned that change in energy = deltaKE + deltaPE + Wdoneonsystem, or if all work is done on the system (none by the system), change in energy = Wdone= deltaKE + deltaPE. • Where does 1/2 come from? • why is the cosine theta needed in some cases, and not in other cases? I noticed that cosine theta was taken out during the net work formula, and wanted to know why? Thank you!   