# Introduction to Work

by Jared Rovny

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00:01 So now we've discussed how objects move on their own, how they act under the influence of different forces as well as the energy that objects have, whether it's kinetic or potential.

00:12 Now, we're going to discuss work.

00:14 So briefly as an overview, like I said so you can see the equations all in one place, we started with the equations of motion, how things move, and then applied forces to those objects to find the accelerations that they experience.

00:25 And then we talked about torque and how we could apply force that would cause something to rotate, and then we discussed just recently the energy, whether it's kinetic energy, potential energy from a spring or from gravity, as well as the total energy which is the sum of the kinetic and potential energy.

00:41 Now we're going to discuss work and the idea of work, the concept of work we're going to discuss is sometimes a little bit counterintuitive so I highly recommend for the next few lectures, you're very careful, take some notes, and then just really give it some time to sink in and work over some example problems because there's a lot of things that might be counterintuitive about the idea of work, it's slightly more challenging in idea, so just really give it the practice it needs and when it makes sense, it will be very helpful for future problems.

01:10 Once we've discussed work, as I've said, we'll go to momentum, but we'll start with work right now.

01:14 First of all, let's take the idea of, one more time, an apple.

01:19 And we're going to apply a force to our apple and that apple is going to move a certain distance deep.

01:24 If I took the force which is say 10 Newtons as an example and I applied that force over a certain distance like 5 meters, if I multiply a force by a distance, it turns out that the units of the force times the distance are units of energy.

01:37 So, we have 50 joules of energy and what this is saying is that the force that we've applied to our object is giving our object energy.

01:44 That's one way to think about what work is.

01:47 It's trying to tell you how much energy is being given to an object by applying a force to that object.

01:52 Specifically, we have an equation for force which is a force times a distance, also the cosine of theta here, but when you think of work, really what you should think is a force times a distance is an energy.

02:05 This is the idea you should have in your head for work.

02:07 We'll get into a lot of the nuances and the intricacies and subtleties of how to use work in different scenarios but just as a basic idea for what work is in a physics context, it's a force applied over a distance which has units of energy.

02:21 So, let's get into some of the details of what work is.

02:25 So work first of all, the units of work as I mentioned are units of joules, of energy.

02:31 So, if you take a force, kilograms meters per second squared multiplied by a distance, meters, you get kilograms meters squared per second squared which is our unit for joules.

02:40 So it is an energy unit. And like energy, work is also a scalar, it's just a number.

02:45 So, we will use vectors like the force vector, the arrow, and the distance vector, which is also an arrow, meaning we'll use distances with directions but these distances, once we've put them all together to find what work is, then work is just a number.

03:00 So, we'll see that as we go forward. It's just a number like 5 joules or 10 joules or something like this.

03:06 There's one more nuance here which is that we have a cosine of theta term in the expression for work and the reason that's there is because work only cares about a force in the direction of the displacement, only in the direction of our motion.

03:19 So to find the amount of force in the direction of our motion, you can see in the example here where I have a force being applied at some angle, but the distance, the direction that the object is actually moving, is in a different direction.

03:30 It's actually moving towards the right rather than off at an angle, and this might be because there are other forces acting on the problem, keeping it from going in the direction of the force as shown here.

03:40 But for whatever reason that this force is at an angle to the direction of motion, we can find the force component in the direction of motion just by again considering a triangle.

03:51 So, if you look at the triangle that we formed here with the force and the direction of motion and we have an angle theta, we can find the component, the horizontal component of the force by once again taking the magnitude of the force and multiplying by cosine of theta.

04:05 And so really, this is just a long fancy way of saying that when you're considering a force and a distance, you only want the force in the direction of motion and to do that you'll find the cosine of the angle between your direction of motion and the force.

### About the Lecture

The lecture Introduction to Work by Jared Rovny is from the course Work.

### Included Quiz Questions

1. mv^2
2. ma
3. mv^2/r
4. mx^2v
5. ma^2/r
1. 30 J
2. 30cos (θ) N
3. 15 J
4. 15cos (θ) N
5. No work was done
1. No work was done
2. 50cos (θ) N
3. 25 J
4. 25cos (θ) N
5. 50 J

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